This question tests your ability to recognize when a relationship has constant rate of change—the defining characteristic of linear functions. Constant rate of change means that for every unit increase in x, y changes by the same amount every time: if Δy/Δx = 5 for one interval and also 5 for every other equal interval, the rate is constant at 5. This constant rate is exactly what makes a function linear (y = mx + b where m is that constant rate). Only linear functions have this property—quadratics, exponentials, and other nonlinear functions have rates that vary at different x-values! Table 1 has Δy=3,3,3 constant; Table 2 has ratios 2,2,2 constant but differences 2,4,8 varying. Choice C correctly identifies only Table 1 has constant rate because its first differences are equal, making it linear. Choice B confuses constant ratio (exponential) with constant rate—Table 2 is exponential, not linear! The three-method constant rate test: METHOD 1 (from table): Calculate Δy/Δx for each pair of consecutive points with equal Δx. All equal? Constant rate. Vary? Non-constant. METHOD 2 (from graph): Is it a straight line? Yes = constant rate. Curved? Non-constant. METHOD 3 (from formula): Is it y = mx + b form? Yes = constant rate m. Any other form (x², $b^x$, etc.)? Non-constant. Pick the method matching your representation! Don't confuse constant RATE with constant RATIO: constant rate (Δy/Δx equal) characterizes linear functions, constant ratio (y₂/y₁ equal) characterizes exponential functions. Check BOTH in a table: if differences are 3, 3, 3 → linear with rate 3. If ratios are 2, 2, 2 → exponential with base 2. If neither constant → some other type. Knowing which pattern to look for prevents confusing linear with exponential growth!

This question tests your ability to recognize when a relationship has constant rate of change—the defining characteristic of linear functions. Constant rate of change means that for every unit increase in x, y changes by the same amount every time: if Δy/Δx = 5 for one interval and also 5 for every other equal interval, the rate is constant at 5. This constant rate is exactly what makes a function linear (y = mx + b where m is that constant rate). Only linear functions have this property—quadratics, exponentials, and other nonlinear functions have rates that vary at different x-values! The model C=15+0.10x is linear, so constant rate 0.10. Choice B correctly identifies the constant rate of 0.10 because it's y=mx+b form, modeling linear cost. Choice A wrongly assumes a fixed fee means non-constant rate, but the fee is the b (constant), not affecting the steady per-text rate m! The three-method constant rate test: METHOD 1 (from table): Calculate Δy/Δx for each pair of consecutive points with equal Δx. All equal? Constant rate. Vary? Non-constant. METHOD 2 (from graph): Is it a straight line? Yes = constant rate. Curved? Non-constant. METHOD 3 (from formula): Is it y = mx + b form? Yes = constant rate m. Any other form (x², $b^x$, etc.)? Non-constant. Pick the method matching your representation! Don't confuse constant RATE with constant RATIO: constant rate (Δy/Δx equal) characterizes linear functions, constant ratio (y₂/y₁ equal) characterizes exponential functions. Check BOTH in a table: if differences are 3, 3, 3 → linear with rate 3. If ratios are 2, 2, 2 → exponential with base 2. If neither constant → some other type. Knowing which pattern to look for prevents confusing linear with exponential growth!

This question tests your ability to recognize when a relationship has constant rate of change—the defining characteristic of linear functions. Constant rate of change means that for every unit increase in x, y changes by the same amount every time: if Δy/Δx = 5 for one interval and also 5 for every other equal interval, the rate is constant at 5. This constant rate is exactly what makes a function linear (y = mx + b where m is that constant rate). Only linear functions have this property—quadratics, exponentials, and other nonlinear functions have rates that vary at different x-values! The formula f(x)=4x-7 is in y=mx+b form, so constant rate m=4. Choice A correctly identifies the constant rate of 4 because it's linear, and negatives don't affect rate constancy. A distractor like Choice C might confuse the y-intercept -7 with the rate, but rate is the coefficient of x! The three-method constant rate test: METHOD 1 (from table): Calculate Δy/Δx for each pair of consecutive points with equal Δx. All equal? Constant rate. Vary? Non-constant. METHOD 2 (from graph): Is it a straight line? Yes = constant rate. Curved? Non-constant. METHOD 3 (from formula): Is it y = mx + b form? Yes = constant rate m. Any other form (x², $b^x$, etc.)? Non-constant. Pick the method matching your representation! Don't confuse constant RATE with constant RATIO: constant rate (Δy/Δx equal) characterizes linear functions, constant ratio (y₂/y₁ equal) characterizes exponential functions. Check BOTH in a table: if differences are 3, 3, 3 → linear with rate 3. If ratios are 2, 2, 2 → exponential with base 2. If neither constant → some other type. Knowing which pattern to look for prevents confusing linear with exponential growth!

This question tests your ability to recognize when a relationship has constant rate of change—the defining characteristic of linear functions. Constant rate of change means that for every unit increase in x, y changes by the same amount every time: if Δy/Δx = 5 for one interval and also 5 for every other equal interval, the rate is constant at 5. This constant rate is exactly what makes a function linear (y = mx + b where m is that constant rate). Only linear functions have this property—quadratics, exponentials, and other nonlinear functions have rates that vary at different x-values! Δd for Δt=2 are 10,10,10, all equal, so Δd/Δt=5 constantly. Choice A correctly identifies the constant rate of 5 because the ratios are equal over equal intervals. Choice C mistakes Δd=10 for the rate, but divide by Δt=2 to get the actual rate 5—always compute Δy/Δx! The three-method constant rate test: METHOD 1 (from table): Calculate Δy/Δx for each pair of consecutive points with equal Δx. All equal? Constant rate. Vary? Non-constant. METHOD 2 (from graph): Is it a straight line? Yes = constant rate. Curved? Non-constant. METHOD 3 (from formula): Is it y = mx + b form? Yes = constant rate m. Any other form (x², $b^x$, etc.)? Non-constant. Pick the method matching your representation! Don't confuse constant RATE with constant RATIO: constant rate (Δy/Δx equal) characterizes linear functions, constant ratio (y₂/y₁ equal) characterizes exponential functions. Check BOTH in a table: if differences are 3, 3, 3 → linear with rate 3. If ratios are 2, 2, 2 → exponential with base 2. If neither constant → some other type. Knowing which pattern to look for prevents confusing linear with exponential growth!

This question tests your ability to recognize when a relationship has constant rate of change—the defining characteristic of linear functions. Constant rate of change means that for every unit increase in x, y changes by the same amount every time: if Δy/Δx = 5 for one interval and also 5 for every other equal interval, the rate is constant at 5. This constant rate is exactly what makes a function linear (y = mx + b where m is that constant rate). Only linear functions have this property—quadratics, exponentials, and other nonlinear functions have rates that vary at different x-values! Here, ΔV for Δt=1 are 3,4,5,6, which vary, so non-constant rate. Choice B correctly identifies the non-constant rate because the ΔV values are not equal, indicating nonlinear. A mistake like in Choice A is averaging varying differences, but for constant rate, they must be identical, not averaged! The three-method constant rate test: METHOD 1 (from table): Calculate Δy/Δx for each pair of consecutive points with equal Δx. All equal? Constant rate. Vary? Non-constant. METHOD 2 (from graph): Is it a straight line? Yes = constant rate. Curved? Non-constant. METHOD 3 (from formula): Is it y = mx + b form? Yes = constant rate m. Any other form (x², $b^x$, etc.)? Non-constant. Pick the method matching your representation! Don't confuse constant RATE with constant RATIO: constant rate (Δy/Δx equal) characterizes linear functions, constant ratio (y₂/y₁ equal) characterizes exponential functions. Check BOTH in a table: if differences are 3, 3, 3 → linear with rate 3. If ratios are 2, 2, 2 → exponential with base 2. If neither constant → some other type. Knowing which pattern to look for prevents confusing linear with exponential growth!

This question tests your ability to recognize when a relationship has constant rate of change—the defining characteristic of linear functions. Constant rate of change means that for every unit increase in x, y changes by the same amount every time: if Δy/Δx = 5 for one interval and also 5 for every other equal interval, the rate is constant at 5. This constant rate is exactly what makes a function linear (y = mx + b where m is that constant rate). Only linear functions have this property—quadratics, exponentials, and other nonlinear functions have rates that vary at different x-values! Plan 1: total =10+5m, linear with constant Δcost/Δmonth=5; Plan 2: 5,10,20,40..., differences 5,10,20 varying (ratios=2 constant, exponential). Choice A correctly identifies only Plan 1 as constant rate because of equal additions, linear growth. Choice B mistakes Plan 2's constant ratio (multiplying by 2) for constant rate—remember to check differences for linear, ratios for exponential, to distinguish them! The three-method constant rate test: METHOD 1 (from table): Calculate Δy/Δx for each pair of consecutive points with equal Δx. All equal? Constant rate. Vary? Non-constant. METHOD 2 (from graph): Is it a straight line? Yes = constant rate. Curved? Non-constant. METHOD 3 (from formula): Is it y = mx + b form? Yes = constant rate m. Any other form (x², $b^x$, etc.)? Non-constant. Pick the method matching your representation! Don't confuse constant RATE with constant RATIO: constant rate (Δy/Δx equal) characterizes linear functions, constant ratio (y₂/y₁ equal) characterizes exponential functions. Check BOTH in a table: if differences are 3, 3, 3 → linear with rate 3. If ratios are 2, 2, 2 → exponential with base 2. If neither constant → some other type. Knowing which pattern to look for prevents confusing linear with exponential growth!

This question tests your ability to recognize when a relationship has constant rate of change—the defining characteristic of linear functions. Constant rate of change means that for every unit increase in x, y changes by the same amount every time: if Δy/Δx = 5 for one interval and also 5 for every other equal interval, the rate is constant at 5. This constant rate is exactly what makes a function linear (y = mx + b where m is that constant rate). Only linear functions have this property—quadratics, exponentials, and other nonlinear functions have rates that vary at different x-values! Situation (a) fills 4 gallons per minute, so constant Δgallons/Δtime=4, linear; (b) area A=s², rate dA/ds=2s varies with s, quadratic; (c) doubles hourly, constant ratio 2 but varying differences (e.g., 1 to 2, +1; 2 to 4, +2), exponential. Choice A correctly identifies only (a) as having constant rate because it's additive growth, equivalent to linear. For (c), a common error is thinking doubling is constant rate, but that's constant ratio—calculate differences to confirm they increase, not stay equal! The three-method constant rate test: METHOD 1 (from table): Calculate Δy/Δx for each pair of consecutive points with equal Δx. All equal? Constant rate. Vary? Non-constant. METHOD 2 (from graph): Is it a straight line? Yes = constant rate. Curved? Non-constant. METHOD 3 (from formula): Is it y = mx + b form? Yes = constant rate m. Any other form (x², $b^x$, etc.)? Non-constant. Pick the method matching your representation! Don't confuse constant RATE with constant RATIO: constant rate (Δy/Δx equal) characterizes linear functions, constant ratio (y₂/y₁ equal) characterizes exponential functions. Check BOTH in a table: if differences are 3, 3, 3 → linear with rate 3. If ratios are 2, 2, 2 → exponential with base 2. If neither constant → some other type. Knowing which pattern to look for prevents confusing linear with exponential growth!

This question tests your ability to recognize when a relationship has constant rate of change—the defining characteristic of linear functions. Constant rate of change means that for every unit increase in x, y changes by the same amount every time: if Δy/Δx = 5 for one interval and also 5 for every other equal interval, the rate is constant at 5. This constant rate is exactly what makes a function linear (y = mx + b where m is that constant rate). Only linear functions have this property—quadratics, exponentials, and other nonlinear functions have rates that vary at different x-values! The formula d=6t+1 is in mx+b form with m=6, so constant rate of 6; for example, from t=0 to 1, Δd=(6*1+1)-(1)=7-1=6; t=1 to 2, (12+1)- (6+1)=13-7=6—constant. Choice A correctly identifies the constant rate of 6 and linear type because it's mx+b form. Choice B incorrectly blames the +1 for non-constancy, but constants affect intercept, not rate—focus on the coefficient of t for the rate! The three-method constant rate test: METHOD 1 (from table): Calculate Δy/Δx for each pair of consecutive points with equal Δx. All equal? Constant rate. Vary? Non-constant. METHOD 2 (from graph): Is it a straight line? Yes = constant rate. Curved? Non-constant. METHOD 3 (from formula): Is it y = mx + b form? Yes = constant rate m. Any other form (x², $b^x$, etc.)? Non-constant. Pick the method matching your representation! Don't confuse constant RATE with constant RATIO: constant rate (Δy/Δx equal) characterizes linear functions, constant ratio (y₂/y₁ equal) characterizes exponential functions. Check BOTH in a table: if differences are 3, 3, 3 → linear with rate 3. If ratios are 2, 2, 2 → exponential with base 2. If neither constant → some other type. Knowing which pattern to look for prevents confusing linear with exponential growth!

This question tests your ability to recognize when a relationship has constant rate of change—the defining characteristic of linear functions. Constant rate of change means that for every unit increase in x, y changes by the same amount every time: if Δy/Δx = 5 for one interval and also 5 for every other equal interval, the rate is constant at 5. This constant rate is exactly what makes a function linear (y = mx + b where m is that constant rate). Only linear functions have this property—quadratics, exponentials, and other nonlinear functions have rates that vary at different x-values! For f(x)=3x²-6x+1, it's quadratic (degree 2, not 1), so the rate varies; for example, from x=0 to 1, Δf=(3-6+1)-(1)= -2 to -1? Wait, f(0)=1, f(1)=3-6+1=-2, Δf=-3; f(2)=12-12+1=1, Δf from 1 to 2=3—not constant. Choice B correctly identifies it as quadratic and thus non-constant rate because it's not in mx+b form. A distractor like choice A might misread the -6x term as the constant rate, but ignore the x² which makes the rate change—always check the highest degree for linearity! The three-method constant rate test: METHOD 1 (from table): Calculate Δy/Δx for each pair of consecutive points with equal Δx. All equal? Constant rate. Vary? Non-constant. METHOD 2 (from graph): Is it a straight line? Yes = constant rate. Curved? Non-constant. METHOD 3 (from formula): Is it y = mx + b form? Yes = constant rate m. Any other form (x², $b^x$, etc.)? Non-constant. Pick the method matching your representation! Don't confuse constant RATE with constant RATIO: constant rate (Δy/Δx equal) characterizes linear functions, constant ratio (y₂/y₁ equal) characterizes exponential functions. Check BOTH in a table: if differences are 3, 3, 3 → linear with rate 3. If ratios are 2, 2, 2 → exponential with base 2. If neither constant → some other type. Knowing which pattern to look for prevents confusing linear with exponential growth!

This question tests your ability to recognize when a relationship has constant rate of change—the defining characteristic of linear functions. Constant rate of change means that for every unit increase in x, y changes by the same amount every time: if Δy/Δx = 5 for one interval and also 5 for every other equal interval, the rate is constant at 5. This constant rate is exactly what makes a function linear (y = mx + b where m is that constant rate). Only linear functions have this property—quadratics, exponentials, and other nonlinear functions have rates that vary at different x-values! For this table, calculate the rates: from t=0 to 2, Δd=1-0=1 and Δt=2, rate=1/2; from t=2 to 4, Δd=4-1=3, rate=3/2; from t=4 to 6, Δd=9-4=5, rate=5/2—these vary, so non-constant rate. Choice B correctly identifies the non-constant rates of 1/2, 3/2, 5/2 because the differences increase, indicating a nonlinear (quadratic) relationship. A distractor like choice C might confuse the increasing differences (1,3,5) as a sign of constancy, but remember, for constant rate, the first differences must be equal, not the second differences (which are constant in quadratics)—focus on first differences for linearity! The three-method constant rate test: METHOD 1 (from table): Calculate Δy/Δx for each pair of consecutive points with equal Δx. All equal? Constant rate. Vary? Non-constant. METHOD 2 (from graph): Is it a straight line? Yes = constant rate. Curved? Non-constant. METHOD 3 (from formula): Is it y = mx + b form? Yes = constant rate m. Any other form (x², $b^x$, etc.)? Non-constant. Pick the method matching your representation! Don't confuse constant RATE with constant RATIO: constant rate (Δy/Δx equal) characterizes linear functions, constant ratio (y₂/y₁ equal) characterizes exponential functions. Check BOTH in a table: if differences are 3, 3, 3 → linear with rate 3. If ratios are 2, 2, 2 → exponential with base 2. If neither constant → some other type. Knowing which pattern to look for prevents confusing linear with exponential growth!