8th Grade Math Flashcards: Construct And Interpret Linear Functions

What this deck covers

This deck focuses on Construct And Interpret Linear Functions, giving you a quick way to review the definitions, rules, and examples that matter most for 8th Grade Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the slope of the line through $(2,5)$ and $(6,13)$?

Answer: $m = 2$. Use m = rac{13-5}{6-2} = rac{8}{4} = 2.

Flashcard 2: A gym membership costs $20$ to join and $15$ per month. What is the initial value in this model?

Answer: $20$. The joining fee is the cost when months = 0.

Flashcard 3: Write the equation of the line passing through $(0,-4)$ and $(5,1)$.

Answer: $y=x-4$. Slope is $\frac{1-(-4)}{5-0}=1$, and $b=-4$ from $(0,-4)$.

Flashcard 4: What is the slope (rate of change) formula using two points $(x_1,y_1)$ and $(x_2,y_2)$?

Answer: $m=\frac{y_2-y_1}{x_2-x_1}$. Rise over run: change in $y$ divided by change in $x$.

Flashcard 5: A runner’s distance is $d=6t+2$ (miles). What does the $2$ mean in context?

Answer: The runner started $2$ miles from the starting point at $t=0$. The constant term represents starting position.

Flashcard 6: In $y=mx+b$, what does $m$ represent in a real-world situation?

Answer: $m$ is the rate of change (change in $y$ per $1$ unit of $x$). Slope tells how much $y$ changes for each unit increase in $x$.

Flashcard 7: A tank has $50$ liters and drains $4$ liters per minute. What is $V(t)$ after $t$ minutes?

Answer: $V(t)=50-4t$. Initial volume minus drain rate times time.

Flashcard 8: A taxi charges a \3$start fee plus$$2$per mile. What is the function for cost$C$vs. miles$m$?

Answer: $C=2m+3$. Fixed fee is initial value, per-mile rate is slope.

Flashcard 9: What is the slope-intercept form of a linear function?

Answer: $y=mx+b$. Standard form where $m$ is slope and $b$ is $y$-intercept.

Flashcard 10: Find the function rule for the linear relationship with points $(3,-1)$ and $(7,11)$.

Answer: $y=3x-10$. Slope is $\frac{11-(-1)}{7-3}=3$; use point to find $b=-10$.

Flashcard 11: Find the slope of the line through $(2,5)$ and $(6,13)$.

Answer: $m=2$. $m=\frac{13-5}{6-2}=\frac{8}{4}=2$

Flashcard 12: From the table points $(1,4)$ and $(4,13)$, what is the rate of change?

Answer: $m=3$. $m=\frac{13-4}{4-1}=\frac{9}{3}=3$

Flashcard 13: Which point on a graph gives the initial value of a linear function?

Answer: The $y$-intercept, $(0,b)$. When $x=0$, $y=b$, which is the initial value.

Flashcard 14: Identify the slope of the line given by $y=-3x+7$.

Answer: $m=-3$. The coefficient of $x$ in slope-intercept form is the slope.

Flashcard 15: In $y=mx+b$, what does $b$ represent in a real-world situation?

Answer: $b$ is the initial value (the $y$-value when $x=0$). The $y$-intercept is the starting value when input is zero.

Flashcard 16: Identify the initial value for the function $y=4x-9$.

Answer: $b=-9$. The constant term in slope-intercept form is the initial value.

Flashcard 17: Write the linear function for a line with slope $m=-2$ and $y$-intercept $b=6$.

Answer: $y=-2x+6$. Substitute slope and $y$-intercept into $y=mx+b$.

Flashcard 18: What is the $y$-intercept of a linear function in terms of a point on its graph?

Answer: The point where $x=0$, written as $(0,b)$. The $y$-intercept occurs where the line crosses the $y$-axis.

Flashcard 19: Find $b$ for a line with slope $m=3$ that passes through $(2,11)$.

Answer: $b=5$. Use $11=3(2)+b$, so $11=6+b$, thus $b=5$.

Flashcard 20: What is the meaning of a negative slope for a linear relationship?

Answer: As $x$ increases, $y$ decreases at a constant rate. Negative slope means the line goes down from left to right.

Flashcard 21: What does $m$ represent in $y=mx+b$ in a real-world situation?

Answer: rate of change per $1$ unit increase in $x$. Slope tells how much $y$ changes for each unit increase in $x$.

Flashcard 22: Find $b$ for the line with $m=3$ that passes through $(2,7)$.

Answer: $b=1$. Substitute into $7=3(2)+b$ to get $b=1$.

Flashcard 23: A tank has $50$ liters and drains $4$ liters per minute. What is the function $V(t)$?

Answer: $V(t)=-4t+50$. Starting volume minus drain rate times minutes.

Flashcard 24: Interpret $m=-3$ in $y=-3x+10$ for a real situation where $x$ is hours and $y$ is dollars.

Answer: dollars decrease by $3$ each hour. Negative slope means decreasing relationship.

Flashcard 25: Interpret $b=8$ in $y=1.5x+8$ when $x$ is minutes and $y$ is pages read.

Answer: at $x=0$, $y=8$ pages already read. The $y$-intercept shows the starting point before timing begins.

Flashcard 26: On a graph, a line crosses the $y$-axis at $(0,5)$ and rises $2$ for every run of $1$. What is $y=$?

Answer: $y=2x+5$. Rise of $2$ over run of $1$ gives slope $m=2$; crosses at $(0,5)$ so $b=5$.

Flashcard 27: A table shows $x: 0,2,4$ and $y: 3,7,11$. What is the rate of change?

Answer: $m=2$. $y$ increases by $4$ when $x$ increases by $2$, so $m=2$.

Flashcard 28: What does $b$ represent in $y=mx+b$ in a real-world situation?

Answer: initial value (starting amount) when $x=0$. The $y$-intercept represents the starting value before any change occurs.

Flashcard 29: Using the table $x: 0,2,4$ and $y: 3,7,11$, what is the initial value?

Answer: $b=3$. When $x=0$, $y=3$ is the initial value.

Flashcard 30: A line passes through $(0,-2)$ and $(4,6)$. What is the linear function $y=$?

Answer: $y=2x-2$. $m=\frac{6-(-2)}{4-0}=2$; $y$-intercept is $-2$.