8th Grade Math Flashcards: Interpret Linear Function Equations

What this deck covers

This deck focuses on Interpret Linear Function Equations, 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: Identify whether $y=\frac{1}{2}x-7$ is linear.

Answer: Linear. It's in the form $y=mx+b$ with $m=\frac{1}{2}$ and $b=-7$.

Flashcard 2: Which set of points is on a straight line: $(0,1),(1,3),(2,5)$ or $(1,1),(2,4),(3,9)$?

Answer: $(0,1),(1,3),(2,5)$. Check if slope is constant between all pairs.

Flashcard 3: Identify the constant rate of change for the points $(1,2)$ and $(4,11)$.

Answer: m=rac{11-2}{4-1}=3. Use the slope formula with the given points.

Flashcard 4: What is the slope of a horizontal line written as $y = 4$?

Answer: $m=0$. Horizontal lines have no change in y.

Flashcard 5: What is the $y$-intercept point for the equation $y = mx + b$?

Answer: $(0,b)$. When $x=0$, $y=b$ in the equation.

Flashcard 6: Identify the $y$-intercept of the line given by $y = -3x + 5$.

Answer: $b=5$. The constant term is the y-intercept.

Flashcard 7: Which function is not linear because it has an exponent on the input: $A=s^2$ or $P=4s$?

Answer: $A=s^2$. Squaring the input makes it nonlinear.

Flashcard 8: Find $b$ if the line has slope $m=2$ and passes through $(0,-5)$ in $y=mx+b$.

Answer: $b=-5$. The y-intercept is the y-value at $x=0$.

Flashcard 9: Identify whether the points $(0,0)$, $(2,4)$, and $(3,6)$ represent a linear relationship.

Answer: Yes; the slope is constant ($m=2$). Calculate slopes: all equal $2$.

Flashcard 10: Which equation has a constant rate of change: y = -rac{1}{2}x + 3 or $y = x^2 - 1$?

Answer: y = -rac{1}{2}x + 3. First-degree equations have constant rates.

Flashcard 11: Which equation is not linear: $y = 5x - 2$ or y = rac{3}{x}?

Answer: y = rac{3}{x}. Division by x creates a curve, not a line.

Flashcard 12: What is the graph of any equation in the form $y = mx + b$?

Answer: A straight line. Linear equations always produce straight lines.

Flashcard 13: What is the meaning of $m$ in the linear equation $y = mx + b$?

Answer: $m$ is the slope (rate of change) of the line. It determines how steep the line is and its direction.

Flashcard 14: Identify whether $y = 7$ is linear.

Answer: Yes; it is linear with $m=0$ and $b=7$. Horizontal lines are linear with zero slope.

Flashcard 15: What is the meaning of $b$ in the linear equation $y = mx + b$?

Answer: $b$ is the $y$-intercept (the value of $y$ when $x=0$). It's where the line crosses the y-axis.

Flashcard 16: Which equation is linear: $y = 2x + 1$ or $y = x^2 + 1$?

Answer: $y = 2x + 1$. Only first-degree equations are linear.

Flashcard 17: What is the definition of a linear function in terms of rate of change?

Answer: A function with a constant rate of change. The slope remains the same between any two points.

Flashcard 18: Identify whether $y = x^3$ is linear.

Answer: No; it is not linear. Powers greater than 1 create curves.

Flashcard 19: What is the output when $x=3$ for the function $y = 2x - 1$?

Answer: $y=5$. Substitute: $y = 2(3) - 1 = 6 - 1$.

Flashcard 20: What is the slope of the vertical line $x=-2$?

Answer: Undefined slope. Vertical lines have infinite steepness, so slope is undefined.

Flashcard 21: Which equation represents a vertical line: $y=4$ or $x=4$?

Answer: $x=4$. Vertical lines have constant $x$-values.

Flashcard 22: Which equation represents a horizontal line: $y=4$ or $x=4$?

Answer: $y=4$. Horizontal lines have constant $y$-values.

Flashcard 23: Identify whether $y=x^2-1$ is linear or not linear.

Answer: Not linear. The $x^2$ term makes it quadratic, not linear.

Flashcard 24: Identify the slope of the line given by $y=-3x+5$.

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

Flashcard 25: What is the slope 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 between any two points on the line.

Flashcard 26: What is the graph of any linear function $y=mx+b$?

Answer: A straight line. Linear functions always produce straight lines when graphed.

Flashcard 27: What is the slope of the line through $(2,7)$ and $(6,19)$?

Answer: $m=3$. $\frac{19-7}{6-2}=\frac{12}{4}=3$

Flashcard 28: What does $b$ represent in $y=mx+b$?

Answer: $b$ is the $y$-intercept (value when $x=0$). The point where the line crosses the y-axis.

Flashcard 29: What does $m$ represent in $y=mx+b$?

Answer: $m$ is the slope (rate of change). It determines the steepness and direction of the line.

Flashcard 30: What is the slope of the line through $(1,4)$ and $(5,4)$?

Answer: $m=0$. Horizontal lines have zero slope since $y$ doesn't change.