8th Grade Math Flashcards: Derive Linear Equations Using Slope

What this deck covers

This deck focuses on Derive Linear Equations Using Slope, 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: Find the slope of a line that rises $12$ units while running $-3$ units.

Answer: $m=-4$. $m=\frac{12}{-3}=-4$ using rise over run.

Flashcard 2: Find the slope of the line through $(2,3)$ and $(6,11)$.

Answer: $m=2$. $m=\frac{11-3}{6-2}=\frac{8}{4}=2$

Flashcard 3: Find the slope of the line through $(-1,4)$ and $(3,2)$.

Answer: $m=-\frac{1}{2}$. $m=\frac{2-4}{3-(-1)}=\frac{-2}{4}=-\frac{1}{2}$

Flashcard 4: Find the equation in the form $y=mx$ for a line through the origin and $(5,-10)$.

Answer: $y=-2x$. $m=\frac{-10-0}{5-0}=-2$, so $y=-2x$

Flashcard 5: Find the equation of the line with slope $m=-4$ passing through $(0,7)$.

Answer: $y=-4x+7$. Point $(0,7)$ is the y-intercept, so $b=7$.

Flashcard 6: What is the equation of a line through the origin with slope $m$?

Answer: $y=mx$. No y-intercept term since the line passes through $(0,0)$.

Flashcard 7: What is slope $m$ defined as in terms of rise and run on a coordinate plane?

Answer: $m=\frac{\text{rise}}{\text{run}}$. Vertical change over horizontal change between two points.

Flashcard 8: What condition on the points makes the slope formula undefined (a vertical line)?

Answer: $x_2-x_1=0$. When denominators equal zero, division is undefined.

Flashcard 9: Find $b$ for a line with slope $m=2$ that passes through $(3,1)$ in $y=mx+b$.

Answer: $b=-5$. Substitute $(3,1)$: $1=2(3)+b$, so $b=1-6=-5$

Flashcard 10: Find the slope $m$ of the line $y=-\frac{3}{5}x+8$.

Answer: $m=-\frac{3}{5}$. The coefficient of $x$ is the slope in slope-intercept form.

Flashcard 11: What point on the coordinate plane represents the $y$-intercept $b$ of $y=mx+b$?

Answer: $(0,b)$. The y-intercept occurs where $x=0$.

Flashcard 12: What is the slope-intercept form of a non-vertical line with slope $m$ and $y$-intercept $b$?

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

Flashcard 13: Find the $y$-intercept $b$ of the line $y=\frac{1}{4}x-6$.

Answer: $b=-6$. The constant term is the y-intercept in slope-intercept form.

Flashcard 14: Which property of similar triangles makes slope constant along a non-vertical line?

Answer: Corresponding side ratios are equal. Similar triangles maintain constant ratios between corresponding sides.

Flashcard 15: What ratio of corresponding sides in right triangles on a line equals the slope $m$?

Answer: $\frac{\Delta y}{\Delta x}$. Change in y over change in x gives the slope.

Flashcard 16: Identify the transformation that maps one slope triangle on a line to another: scaling, reflection, or rotation?

Answer: Scaling (dilation). Triangles scale proportionally along a line, maintaining slope.

Flashcard 17: Find the equation of the line through $(2,-1)$ and $(2,5)$ (state the line equation).

Answer: $x=2$. Same x-coordinates create a vertical line.

Flashcard 18: What is the slope formula between $(x_1, y_1)$ and $(x_2, y_2)$ on a non-vertical line?

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

Flashcard 19: Find the equation in the form $y=mx+b$ with slope $m=3$ and y-intercept $b=-2$.

Answer: $y=3x-2$. Substitute given slope and y-intercept into slope-intercept form.

Flashcard 20: Identify $m$ and $b$ for the line $y=-2x+7$.

Answer: $m=-2$, $b=7$. Read coefficient of $x$ for slope, constant for y-intercept.

Flashcard 21: Find the equation of the line with slope $\frac{1}{2}$ and $y$-intercept $-4$.

Answer: $y=\frac{1}{2}x-4$. Substitute slope and y-intercept into $y=mx+b$.

Flashcard 22: Find the equation of the line through the origin with slope $-3$.

Answer: $y=-3x$. Use $y=mx$ with $m=-3$ for lines through origin.

Flashcard 23: Find the slope between $(-1,4)$ and $(3,0)$.

Answer: $m=-1$. $m=\frac{0-4}{3-(-1)}=\frac{-4}{4}=-1$

Flashcard 24: Identify the geometric fact used to show slope is constant on a line using right triangles.

Answer: Right triangles formed are similar. Similar triangles have proportional sides, ensuring constant slope.

Flashcard 25: What is the $y$-intercept of a line given by $y=mx+b$?

Answer: $b$. In $y=mx+b$, the constant term is the y-intercept.

Flashcard 26: What is the slope of a line given by $y=mx+b$?

Answer: $m$. In $y=mx+b$, the coefficient of $x$ is the slope.

Flashcard 27: What is the slope-intercept form when the line passes through the origin?

Answer: $y=mx$ (because $b=0$). Origin means $(0,0)$, so y-intercept $b=0$.

Flashcard 28: What point is the $y$-intercept $b$ located at on the coordinate plane?

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

Flashcard 29: What is the slope-intercept form of a line with slope $m$ and $y$-intercept $b$?

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

Flashcard 30: What is the slope of a vertical line (no change in $x$)?

Answer: Undefined. Division by zero (run = 0) makes slope undefined.