PSAT Math Flashcards: Linear Functions

What this deck covers

This deck focuses on Linear Functions, giving you a quick way to review the definitions, rules, and examples that matter most for PSAT 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 relationship between slopes of parallel nonvertical lines?

Answer: They are equal: $m_1 = m_2$. Parallel lines have the same slope.

Flashcard 2: What is the equation of a vertical line through $x = a$?

Answer: $x = a$. Vertical lines have constant x-coordinate.

Flashcard 3: Find the equation of the line perpendicular to $y=\frac{1}{4}x-3$ through $(0,2)$.

Answer: $y=-4x+2$. Perpendicular slope is $-4$; passes through $(0,2)$.

Flashcard 4: Find the slope of the line through $(2,5)$ and $(6,1)$.

Answer: $-1$. $m=\frac{1-5}{6-2}=\frac{-4}{4}=-1$.

Flashcard 5: Evaluate the linear function $f(x)=2x-7$ at $x=5$.

Answer: $f(5)=3$. Substitute: $f(5) = 2(5) - 7 = 10 - 7 = 3$.

Flashcard 6: Identify whether $y=7x+1$ is increasing, decreasing, or constant.

Answer: Increasing. Positive slope ($7>0$) means function increases.

Flashcard 7: Find the slope of the line through $(2,7)$ and $(6,-1)$.

Answer: $m=-2$. Apply slope formula: $m = \frac{-1-7}{6-2} = \frac{-8}{4} = -2$.

Flashcard 8: Convert $4x - 5y = 10$ to slope-intercept form.

Answer: $y = \frac{4}{5}x - 2$. Solve for $y$: $y = \frac{4x-10}{5} = \frac{4}{5}x - 2$.

Flashcard 9: What is the slope of a line parallel to a line with slope $m$?

Answer: $m$. Parallel lines have identical slopes.

Flashcard 10: Find the $y$-intercept of the line $2x+3y=12$.

Answer: $4$. Set $x=0$: $3y=12$, so $y=4$.

Flashcard 11: What is the point-slope form of a line with slope $m$ through $(x_1,y_1)$?

Answer: $y-y_1=m(x-x_1)$. Uses a known point and slope to define the line.

Flashcard 12: What is the relationship between slopes of perpendicular nonvertical lines?

Answer: They are negative reciprocals: $m_1m_2 = -1$. Product of perpendicular slopes equals $-1$.

Flashcard 13: Identify the slope and $y$-intercept of $y = -3x + 5$.

Answer: $m=-3$, $b=5$. Read directly from $y = mx + b$ form.

Flashcard 14: What is the slope-intercept form of a linear equation?

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

Flashcard 15: State the formula for slope between $(x_1,y_1)$ and $(x_2,y_2)$.

Answer: $m=\frac{y_2-y_1}{x_2-x_1}$. Rise over run between two points.

Flashcard 16: Find the equation of the line parallel to $y=-2x+7$ through $(3,1)$.

Answer: $y=-2x+7$. Same slope $-2$; use point-slope: $y-1=-2(x-3)$.

Flashcard 17: Find the equation in slope-intercept form of the line with slope $4$ and $y$-intercept $-2$.

Answer: $y = 4x - 2$. Substitute $m$ and $b$ into $y = mx + b$.

Flashcard 18: What do $m$ and $b$ represent in $y=mx+b$?

Answer: $m$ is slope; $b$ is $y$-intercept. Slope determines steepness; $y$-intercept is where line crosses $y$-axis.

Flashcard 19: Find the function value $f(3)$ for $f(x)=-2x+9$.

Answer: $3$. $f(3)=-2(3)+9=-6+9=3$.

Flashcard 20: Find the equation in slope-intercept form through $(0,-4)$ and $(2,0)$.

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

Flashcard 21: What is the slope of a vertical line (written as $x=c$)?

Answer: Undefined. Vertical lines have infinite steepness (division by zero).

Flashcard 22: What is the slope of a line perpendicular to $y = \frac{2}{3}x - 1$?

Answer: $-\frac{3}{2}$. Negative reciprocal of $\frac{2}{3}$ is $-\frac{3}{2}$.

Flashcard 23: What is the slope of a horizontal line (written as $y=c$)?

Answer: $0$. Horizontal lines have no rise, so slope is zero.

Flashcard 24: Find the slope of the line $5x-2y=10$.

Answer: $\frac{5}{2}$. Rewrite as $y=\frac{5}{2}x-5$; slope is coefficient of $x$.

Flashcard 25: Identify the $x$-intercept in terms of $m$ and $b$ for $y=mx+b$.

Answer: $x=-\frac{b}{m}$ (if $m\ne 0$). Set $y=0$ and solve for $x$.

Flashcard 26: Find the equation in slope-intercept form of the line with slope $3$ and $y$-intercept $-2$.

Answer: $y=3x-2$. Direct substitution into $y=mx+b$ form.

Flashcard 27: Find the $y$-intercept of $2x + 3y = 12$.

Answer: $(0,4)$. Set $x=0$: $3y=12$, so $y=4$.

Flashcard 28: What is the $x$-intercept of $y = mx + b$ in terms of $m$ and $b$ (with $m \ne 0$)?

Answer: $\left(-\frac{b}{m},0\right)$. Set $y=0$ and solve for $x$.

Flashcard 29: What is the standard form of a linear equation?

Answer: $Ax+By=C$. General form where $A$, $B$, and $C$ are constants.

Flashcard 30: Find the $x$-intercept of $3x - 2y = 6$.

Answer: $(2,0)$. Set $y=0$: $3x=6$, so $x=2$.

Flashcard 31: What is the slope of a line perpendicular to a line with slope $m$?

Answer: $-\frac{1}{m}$ (if $m\ne 0$). Perpendicular slopes multiply to $-1$.

Flashcard 32: What is the $y$-intercept of the line $y = mx + b$?

Answer: $(0,b)$. Where the line crosses the y-axis (when $x=0$).

Flashcard 33: Find the equation of the line with slope $-\frac{1}{2}$ passing through $(4,3)$.

Answer: $y = -\frac{1}{2}x + 5$. Use point-slope form: $y - 3 = -\frac{1}{2}(x - 4)$.