This question tests interpreting y=mx+b as defining a linear function (straight-line graph, constant slope m, y-intercept b) and distinguishing from non-linear functions (curved graphs, variable squared/in denominator/in absolute value/as exponent), by finding the equation from points. Linear function y=mx+b: m is slope (rate of change: y increases by m per unit x), b is y-intercept (initial value when x=0, where line crosses y-axis), graph is straight line through (0,b) with constant slope m. Non-linear functions have x with exponent ≠1, or in denominator, or in other function: y=x² graphs as parabola (curved, points (1,1),(2,4),(3,9) not on straight line), y=1/x graphs as hyperbola (curved), y=|x| is V-shape (not single straight line)—all have non-constant slopes (curvature indicates slope varies). For example, y=3x+2 is linear with straight graph through (0,2) and say (1,5), slope (5-2)/(1-0)=3, versus y=x² through (0,0),(1,1),(2,4) with varying slopes. The correct choice is A, y=3x-4, as b=-4 from (0,-4), m=(2-(-4))/(2-0)=3, fitting y=mx+b with straight line. A common error is interpreting m and b backwards or with wrong signs, like choosing negative slope despite positive rise. To find: (1) use points to calculate m=(y2-y1)/(x2-x1), (2) plug x=0 for b, (3) verify straight line, (4) check constant slope; mistakes include confusing rise/run or thinking points imply non-linear.

This question tests interpreting y=mx+b as defining a linear function (straight-line graph, constant slope m, y-intercept b) and distinguishing from non-linear functions (curved graphs, variable squared/in denominator/in absolute value/as exponent). Linear function y=mx+b: m is slope (rate of change: y increases by m per unit x), b is y-intercept (initial value when x=0, where line crosses y-axis), graph is straight line through (0,b) with constant slope m. Non-linear functions have x with exponent ≠1, or in denominator, or in other function: y=x² graphs as parabola (curved, points (1,1),(2,4),(3,9) not on straight line), y=1/x graphs as hyperbola (curved), y=|x| is V-shape (not single straight line)—all have non-constant slopes (curvature indicates slope varies). For example, y=3x+2 is linear (x to power 1, straight graph), versus y=x² (x squared, curved with non-constant rate). The correct choice is B, y=2x is linear because x is to the first power (fits y=mx+b with m=2, b=0), y=x² is non-linear because x is squared (curved parabola). A common error is thinking y=2x non-linear for lacking b (wrong, b can be 0) or claiming y=x² linear for passing through (0,0). To compare: (1) check form and exponent, (2) graph shape, (3) rate constancy, (4) fit to y=mx+b; mistakes include confusing origins or variables alone as linear.

This question tests interpreting y=mx+b as defining a linear function (straight-line graph, constant slope m, y-intercept b) and distinguishing from non-linear functions (curved graphs, variable squared/in denominator/in absolute value/as exponent), specifically in a real-world context. Linear function y=mx+b: m is slope (rate of change: y increases by m per unit x), b is y-intercept (initial value when x=0, where line crosses y-axis), graph is straight line through (0,b) with constant slope m. Non-linear functions have x with exponent ≠1, or in denominator, or in other function: y=x² graphs as parabola (curved, points (1,1),(2,4),(3,9) not on straight line), y=1/x graphs as hyperbola (curved), y=|x| is V-shape (not single straight line)—all have non-constant slopes (curvature indicates slope varies). For example, y=3x+2 is linear with a straight graph where m=3 means y rises by 3 per x, b=2 is the start, versus y=x² with points showing varying increases like from 1 to 4 then to 9. The correct choice is B, where m=2 is the cost per snack (rate) and b=6 is the ticket fee (fixed cost when x=0), matching the model's interpretation. A common error is interpreting m and b backwards, like thinking the fixed fee is the slope, or confusing them with non-cost elements like starting snacks. To identify and interpret: (1) check form y=mx+b for linearity, (2) confirm x to power 1, (3) graph if needed for straight line, (4) calculate constant slope; here, m is the per-unit rate ($2/snack), b is initial value ($6 ticket), with mistakes like ignoring context or claiming non-linear due to positive values.

This question tests interpreting y=mx+b as defining a linear function (straight-line graph, constant slope m, y-intercept b) and distinguishing from non-linear functions (curved graphs, variable squared/in denominator/in absolute value/as exponent). Linear function y=mx+b: m is slope (rate of change: y increases by m per unit x), b is y-intercept (initial value when x=0, where line crosses y-axis), graph is straight line through (0,b) with constant slope m. Non-linear functions have x with exponent ≠1, or in denominator, or in other function: y=x² graphs as parabola (curved, points (1,1),(2,4),(3,9) not on straight line), y=1/x graphs as hyperbola (curved), y=|x| is V-shape (not single straight line)—all have non-constant slopes (curvature indicates slope varies). For example, y=3x+2 is linear with single straight graph, versus y=|x| with V-shape from two lines, not fitting one y=mx+b. The correct choice is C, incorrect because it's not a single straight line and can't be one y=mx+b for all x, due to the absolute value causing a bend. A common error is calling y=|x| linear because it's straight pieces (wrong, linearity requires one constant slope, not V-shaped), or thinking b=0 is required. To identify: (1) check if one y=mx+b works for all x, (2) exponent or function like absolute value, (3) graph single straight line, (4) constant slope everywhere; mistakes include equating piecewise straight to linear.

This question tests interpreting y=mx+b as defining a linear function (straight-line graph, constant slope m, y-intercept b) and distinguishing from non-linear functions (curved graphs, variable squared/in denominator/in absolute value/as exponent), by identifying m and b. Linear function y=mx+b: m is slope (rate of change: y increases by m per unit x), b is y-intercept (initial value when x=0, where line crosses y-axis), graph is straight line through (0,b) with constant slope m. Non-linear functions have x with exponent ≠1, or in denominator, or in other function: y=x² graphs as parabola (curved, points (1,1),(2,4),(3,9) not on straight line), y=1/x graphs as hyperbola (curved), y=|x| is V-shape (not single straight line)—all have non-constant slopes (curvature indicates slope varies). For example, y=3x+2 is linear with m=3 (slope) and b=2 (intercept), graphing straight through (0,2), versus y=x² with no constant m. The correct choice is B, y=-4x+7, where m=-4 is the slope and b=7 is the y-intercept, matching the given values. A common error is switching m and b, like choosing y=7x-4, or confusing signs. To interpret: (1) identify coefficient of x as m, constant as b, (2) confirm linear form, (3) graph to verify, (4) check slope sign for direction; mistakes include thinking negative m makes it non-linear.

This question tests interpreting y=mx+b as defining a linear function with straight-line graph, constant slope m from points, and y-intercept b, distinguishing from non-linear not fitting straight lines. Linear y=mx+b: m=(y2-y1)/(x2-x1) constant, b=y when x=0; non-linear like y=x² don't have constant m between points, curving instead of straight. For example, points (0,2),(1,5) give m=3, y=3x+2 linear straight; versus (0,0),(1,1),(2,4) for y=x² with varying m=1 then 3, curved. Here, points (0,-3),(2,1) give m=(1-(-3))/(2-0)=2, b=-3, so y=2x-3 (A) matches the line. Common errors: wrong m like -2 (B) or 1/2 (C), or sign flip to +3 (D), miscalculating slope or intercept. Identifying: (1) compute m from points, (2) find b at x=0, (3) write y=mx+b, (4) verify other points. Interpreting: m rate between points, b start; mistakes: swapping signs or confusing rise/run.

This question tests interpreting y=mx+b as defining a linear function with a straight-line graph and constant slope m, while identifying non-linear functions with curved graphs or non-constant rates, such as those with x squared, in denominators, absolute values, or exponents. Linear functions like y=mx+b have constant slope m (y changes by m per unit x) and y-intercept b, graphing straight through (0,b); non-linear ones vary, e.g., y=x² is a parabola with increasing slope (points (1,1),(2,4),(3,9) show y-differences 3,5—not constant), y=1/x hyperbola, y=|x| V-shape with slope shift. For instance, y=3x+2 is linear with constant rate 3 and straight graph, but y=x² curves with points not collinear, demonstrating variable rate (slope between (0,0)-(1,1) is 1, but (1,1)-(2,4) is 3). The non-linear function here is C, y=x², lacking constant rate and straight graph, while A, B, D are linear in y=mx+b form. Common errors include calling y=x² linear because it has x (ignoring exponent 2 causing curvature) or misinterpreting m and b in linear ones, like swapping slope and intercept. Identifying linear: (1) rewrite as y=mx+b, (2) check x exponent=1, (3) graph for straightness, (4) confirm constant slope via points. Interpreting: m is rate/steepness, b starting value; mistakes: assuming all variable equations are linear or claiming curved graphs have constant rates.

This question tests interpreting y=mx+b by identifying the equation matching given slope m and y-intercept b, ensuring it's linear with straight graph and constant rate. In y=mx+b, m is slope (rate, sign for direction: positive up-right, negative down-right), b y-value at x=0; non-linear differ, e.g., y=x² has no fixed m, curves. Example: y=3x+2 has m=3 (up 3/right 1), b=2; contrast y=x² with no constant m. With m=-3 (down-right), b=5, equation is y=-3x+5 (B), linear form matching. Errors: positive m (A), swapped values (C), wrong signs/magnitudes (D), confusing roles. Identifying: (1) plug in m,b directly, (2) check form, (3) graph for straight with intercept b, slope m, (4) verify direction. Interpreting: negative m means decreasing; mistakes: sign errors or thinking b is slope.

This question tests interpreting y=mx+b as defining a linear function with a straight-line graph, constant slope m, and y-intercept b, and applying it to real-world contexts like costs, distinguishing from non-linear scenarios. In y=mx+b, m is the slope representing the constant rate of change, such as cost per item, and b is the y-intercept, the fixed initial value like a membership fee when x=0; non-linear functions, like y=x² for accelerating costs or y=1/x for decreasing rates, have varying slopes and curved graphs, e.g., points (1,1), (2,4) for y=x² not aligning straight. For example, y=3x+2 models a scenario with $2 fixed plus $3 per unit, graphing as a straight line from (0,2) rising steadily, versus y=x² which curves and doesn't fit constant-rate situations like ticket pricing. Here, in y=3x+6, m=3 is the cost per ticket (rate) and b=6 is the membership fee (fixed when x=0), correctly identified in choice B, as it matches the description of $6 fee plus $3 per ticket. A common mistake is reversing m and b, like thinking m=6 is the per-ticket cost (choice D), or confusing which is fixed versus variable, ignoring that b is when x=0. To interpret: identify m as the variable rate (slope) and b as the constant (intercept); check by plugging x=0 to find b, and slope as change in y over change in x. Avoid errors like assuming m is fixed because it's first in the equation, or thinking non-linear forms could model constant rates.

This question tests interpreting y=mx+b as defining a linear function (straight-line graph, constant slope m, y-intercept b) and distinguishing from non-linear functions (curved graphs, variable squared/in denominator/in absolute value/as exponent). Linear function y=mx+b: m is slope (rate of change: y increases by m per unit x), b is y-intercept (initial value when x=0, where line crosses y-axis), graph is straight line through (0,b) with constant slope m. Non-linear functions have x with exponent ≠1, or in denominator, or in other function: y=x² graphs as parabola (curved, points (1,1),(2,4),(3,9) not on straight line), y=1/x graphs as hyperbola (curved), y=|x| is V-shape (not single straight line)—all have non-constant slopes (curvature indicates slope varies). For example, y=3x+2 is linear with a straight graph passing through (0,2) and rising 3 units per 1 unit right, whereas y=x² has points like (0,0), (1,1), (2,4) demonstrating curvature as the slope increases. The correct choice is C, concluding it is not linear because the changes in y (2, 2, 4) are not constant for equal Δx=1, indicating varying slope. A common error is mistaking it for linear due to initial constant changes, ignoring the later variation, or confusing with exponential growth. Identifying linear: (1) check form (can write as y=mx+b? yes→linear), (2) check exponent (x¹ only? yes→linear, x², x⁰, x⁻¹ etc.→non-linear), (3) check graph (straight→linear, curved→non-linear), (4) verify constant slope (calculate between multiple point pairs, same→linear, varies→non-linear). Interpreting: m in y=mx+b is slope (rise/run, rate, steepness), b is y-intercept (where x=0, starting value), context meaning (y=3x+20 for cost: 3=$/item, 20=fixed cost). Mistakes: thinking any equation with x,y is linear (ignoring exponents, denominators), confusing m and b roles, claiming curved graphs are linear.