U3D3 Slope-Intercept Form

Vocabulary and key concepts covering linear equations in slope-intercept form, calculating slopes, finding perpendicular lines, and analyzing vertical and horizontal lines.

Slope-Intercept Form

A linear equation written in the form $y = mx + b$, where $m$ represents the slope and $b$ represents the y-intercept.

Slope ($m$)

The ratio representing $\frac{\text{rise}}{\text{run}}$ in a linear equation, which defines the steepness and direction of the line.

y-intercept ($b$)

The point where the graph of an equation intersects the y-axis, represented by the constant $b$ in the equation $y = mx + b$.

Slope-intercept form of $5x + 3y = -12$

$y = -\frac{5}{3}x - 4$, obtained by solving for $y$, yielding a slope of $-\frac{5}{3}$ and a y-intercept of $-4$.

Slope-intercept form of $y - 3 = \frac{2}{3}(x - 5)$

$y = \frac{2}{3}x - \frac{1}{3}$, where the y-intercept is $-\frac{1}{3} = -0.33\dots$.

Perpendicular Slope to $3x + 4y - 6 = 0$

$\frac{4}{3}$, which is perpendicular to the original line's slope of $m = -\frac{3}{4}$.

Equation of the line perpendicular to $3x + 4y - 6 = 0$ with a y-intercept of $4$

$y = \frac{4}{3}x + 4$, which uses the perpendicular slope $\frac{4}{3}$ and the given y-intercept of $4$.

Slope and y-intercept of the line $x - 5 = -3$

The vertical line simplifies to $x = 2$, with a slope of $m = \frac{\text{rise}}{0} = \text{undefined}$ and a y-intercept that does not exist.

Slope and y-intercept of the line $2y - 6 = 5$

The horizontal line simplifies to $y = \frac{11}{2}$, with a slope of $m = \frac{0}{\text{run}} = 0$ and a y-intercept of $b = \frac{11}{2}$.