Equations With Two Variables - SAT Math

Undefined. Vertical lines have undefined slope.

$-\frac{1}{4}$. Perpendicular slopes are negative reciprocals.

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

$-5$. Coefficient of $x$ in slope-intercept form.

The slope is $-5$. The coefficient of $x$ in slope-intercept form.

$y - y_1 = m(x - x_1)$. Uses known point $(x_1, y_1)$ and slope $m$.

$(2, 0)$. Set $y = 0$: $4x = 8$, so $x = 2$.

$y = -\frac{1}{2}x + \frac{7}{2}$. Perpendicular slope $-\frac{1}{2}$, use point-slope form.

$m = \frac{y_2 - y_1}{x_2 - x_1}$. Rise over run formula for any two points.

Yes. Each x-value has exactly one y-value.

Point-slope form. Form $y - y_1 = m(x - x_1)$ with known point.

$x = 2$. Substitute $y = 3$ and solve: $2x + 3 = 7$.

$y = -\frac{2}{3}x + 2$. Solve for $y$ by isolating it on one side.

$y - y_1 = m(x - x_1)$ to $y = mx + b$. Expand point-slope and solve for $y$.

$Ax + By = C$. General form with integer coefficients $A$, $B$, and $C$.

$x = 4$. Set $y = 0$ and solve for $x$.

1. In $y = mx + b$ form, the coefficient of $x$ is the slope.

$3x - y = -5$. Expand and rearrange to $Ax + By = C$ form.

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

1. In $y = mx + b$ form, $b$ is the y-intercept.

Slopes are equal. Parallel lines have identical slopes but different intercepts.

$2$. Use slope formula: $\frac{7-3}{4-2} = \frac{4}{2} = 2$.

$m$. Coefficient of $x$ represents the rate of change.

$(0, 2)$. Set $x = 0$: $6y = 12$, so $y = 2$.

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

$y = 7$. Horizontal lines have constant $y$-values.

$Ax + By = C$. Standard form where A, B, and C are constants.

The x-intercept is $x = 4$.. Set $y = 0$ and solve for $x$.

1. Horizontal lines have zero rise over run.

Undefined. Vertical lines have no finite slope.

$y = 2x - 4$. Isolate $y$ by subtracting $4x$ and dividing by $-2$.

$x = 4$. Undefined slope means vertical line.

$\frac{1}{2}$. Parallel lines have identical slopes.

$-\frac{3}{2}$. Coefficient of $x$ in slope-intercept form.

The y-intercept is $b$. The constant term where the line crosses the y-axis.

$y = -2x + 6$. Use point-slope: $y - 4 = -2(x - 1)$, then solve.

$y = 2x - 4$. Divide both sides by -2 to isolate $y$.

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

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

$y - 1 = 3(x - 1)$. Use point $(1,1)$ in point-slope formula.

$y = 3x - 4$. Direct substitution into $y = mx + b$ form.

$(2, 0)$. Set $y = 0$: $0 = 4x - 8$, so $x = 2$.

$2$. Set $x = 0$: $5y = 10$, so $y = 2$.

Standard form. Form $Ax + By = C$ with integer coefficients.

$x = 3$. Substitute and solve the system of equations.

$y = 5$. Zero slope creates horizontal line.

$x = 5$. Vertical lines have constant $x$-values.

$b$. Constant term where line crosses y-axis.

$y = -\frac{3}{4}x + 3$. Solve for $y$: $4y = -3x + 12$, then $y = -\frac{3}{4}x + 3$.

1. Horizontal lines have zero slope.

$2x + y = 5$. Move $x$-term to left: $2x + y = 5$.

$(0, 4)$. Set $x = 0$: $2y = 8$, so $y = 4$.

$y = -\frac{1}{3}x + 6$. Same slope, different y-intercept through given point.

$y = -\frac{2}{3}x + 2$. Isolate $y$ by subtracting $2x$ and dividing by $3$.

Slope-intercept form. Shows slope $m$ and y-intercept $b$ directly.

$-\frac{3}{2}$. Set $y = 0$: $0 = 2x + 3$, so $x = -\frac{3}{2}$.

$y = -\frac{2}{3}x + 2$. Solve for $y$ by isolating it on one side.

$-5$. Coefficient of $x$ in slope-intercept form.

$2x + y = 5$. Move $x$-term to left: $2x + y = 5$.

The x-intercept is $x = 4$.. Set $y = 0$ and solve for $x$.

The slope is $-5$. The coefficient of $x$ in slope-intercept form.

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

Slope-intercept form. Shows slope $m$ and y-intercept $b$ directly.

$x = 2$. Substitute $y = 3$ and solve: $2x + 3 = 7$.

$y = 2x - 4$. Isolate $y$ by subtracting $4x$ and dividing by $-2$.

The y-intercept is $b$. The constant term where the line crosses the y-axis.

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

$y = -\frac{2}{3}x + 2$. Isolate $y$ by subtracting $2x$ and dividing by $3$.

$Ax + By = C$. General form with integer coefficients $A$, $B$, and $C$.