4.6 Find the Equation of a Line

Before you get started, take this readiness quiz.

Solve: $\frac{2}{3} = \frac{x}{5}$.
If you missed this problem, review the reference.

Simplify: $- \frac{2}{5} \left(x - 15\right)$.
If you missed this problem, review the reference.

Find an equation of a line with slope $\frac{2}{5}$ and y-intercept $\left(0 , 4\right)$.

Find an equation of a line with slope $−1$ and y-intercept $\left(0 , −3\right)$.

Find an equation of a line with slope $m = \frac{5}{6}$ and containing the point $\left(6 , 3\right)$.

Find an equation of a line with slope $m = \frac{2}{3}$ and containing thepoint $\left(9 , 2\right)$.

Find an equation of a line with slope $m = - \frac{2}{5}$ and containing the point $\left(10 , −5\right)$.

Find an equation of a line with slope $m = - \frac{3}{4}$, and containing the point $\left(4 , −7\right)$.

Find an equation of a horizontal line containing the point $\left(−3 , 8\right)$.

Find an equation of a horizontal line containing the point $\left(−1 , 4\right)$.

Find an equation of a line containing the points $\left(3 , 1\right)$ and $\left(5 , 6\right)$.

Find an equation of a line containing the points $\left(1 , 4\right)$ and $\left(6 , 2\right)$.

Find an equation of a line containing the points $\left(−2 , −4\right)$ and $\left(1 , −3\right)$.

Find an equation of a line containing the points $\left(−4 , −3\right)$ and $\left(1 , −5\right)$.

Find an equation of a line that contains the points $\left(−2 , 4\right)$ and $\left(−2 , −3\right)$. Write the equation in slope–intercept form.

Find an equation of a line containing the points $\left(5 , 1\right)$ and $\left(5 , −4\right)$.

Find an equaion of a line containing the points $\left(−4 , 4\right)$ and $\left(−4 , 3\right)$.

Find an equation of a line parallel to the line $y = 3 x + 1$ that contains the point $\left(4 , 2\right)$. Write the equation in slope–intercept form.

Find an equation of a line parallel to the line $y = \frac{1}{2} x - 3$ that contains the point $\left(6 , 4\right)$.

Find an equation of a line perpendicular to the line $y = 3 x + 1$ that contains the point $\left(4 , 2\right)$. Write the equation in slope–intercept form.

Find an equation of a line perpendicular to the line $y = \frac{1}{2} x - 3$ that contains the point $\left(6 , 4\right)$.

Find an equation of a line perpendicular to $x = 5$ that contains the point $\left(3 , −2\right)$. Write the equation in slope–intercept form.

Find an equation of a line that is perpendicular to the line $x = 4$ that contains the point $\left(4 , −5\right)$. Write the equation in slope–intercept form.

Find an equation of a line that is perpendicular to the line $x = 2$ that contains the point $\left(2 , −1\right)$. Write the equation in slope–intercept form.

Find an equation of a line that is perpendicular to $y = −4$ that contains the point $\left(−4 , 2\right)$. Write the equation in slope–intercept form.

Find an equation of a line that is perpendicular to the line $y = 1$ that contains the point $\left(−5 , 1\right)$. Write the equation in slope–intercept form.

Find an equation of a line that is perpendicular to the line $y = −5$ that contains the point $\left(−4 , −5\right)$.

Find the equation of a line with given slope and y-intercept. Write the equation in slope–intercept form.

slope 4 and y-intercept $\left(0 , 1\right)$

Find the equation of a line with given slope and y-intercept. Write the equation in slope–intercept form.

slope 8 and y-intercept $\left(0 , −6\right)$

Find the equation of a line with given slope and y-intercept. Write the equation in slope–intercept form.

slope $−1$ and y-intercept $\left(0 , 7\right)$

Find the equation of a line with given slope and y-intercept. Write the equation in slope–intercept form.

slope $−3$ and y-intercept $\left(0 , −1\right)$

Find the equation of a line with given slope and y-intercept. Write the equation in slope–intercept form.

slope $\frac{1}{5}$ and y-intercept $\left(0 , −5\right)$

Find the equation of a line with given slope and y-intercept. Write the equation in slope–intercept form.

slope $- \frac{2}{3}$ and y-intercept $\left(0 , −3\right)$

Find the equation of a line with given slope and y-intercept. Write the equation in slope–intercept form.

slope 0 and y-intercept $\left(0 , 2\right)$

Find the equation of a line with given slope and y-intercept. Write the equation in slope–intercept form.

slope $−4$ and y-intercept $\left(0 , 0\right)$

Find the equation of a line with given slope and containing the given point. Write the equation in slope–intercept form.

$m = \frac{3}{8}$, point $\left(8 , 2\right)$

Find the equation of a line with given slope and containing the given point. Write the equation in slope–intercept form.

$m = \frac{5}{6}$, point $\left(6 , 7\right)$

Find the equation of a line with given slope and containing the given point. Write the equation in slope–intercept form.

$m = - \frac{3}{5}$, point $\left(10 , −5\right)$

Find the equation of a line with given slope and containing the given point. Write the equation in slope–intercept form.

$m = - \frac{1}{3}$, point $\left(−9 , −8\right)$

Find the equation of a line with given slope and containing the given point. Write the equation in slope–intercept form.

Horizontal line containing $\left(−1 , 4\right)$

Find the equation of a line with given slope and containing the given point. Write the equation in slope–intercept form.

Horizontal line containing $\left(−1 , −7\right)$

Find the equation of a line with given slope and containing the given point. Write the equation in slope–intercept form.

$m = - \frac{5}{2}$, point $\left(−8 , −2\right)$

Find the equation of a line with given slope and containing the given point. Write the equation in slope–intercept form.

$m = −4$, point $\left(−2 , −3\right)$

Find the equation of a line with given slope and containing the given point. Write the equation in slope–intercept form.

Horizontal line containing $\left(4 , −8\right)$

Find the equation of a line containing the given points. Write the equation in slope–intercept form.

$\left(3 , 1\right)$ and $\left(2 , 5\right)$

Find the equation of a line containing the given points. Write the equation in slope–intercept form.

$\left(2 , 7\right)$ and $\left(3 , 8\right)$

Find the equation of a line containing the given points. Write the equation in slope–intercept form.

$\left(−5 , −3\right)$ and $\left(4 , −6\right)$

Find the equation of a line containing the given points. Write the equation in slope–intercept form.

$\left(−2 , 8\right)$ and $\left(−4 , −6\right)$

Find the equation of a line containing the given points. Write the equation in slope–intercept form.

$\left(3 , −2\right)$ and $\left(−4 , 4\right)$

Find the equation of a line containing the given points. Write the equation in slope–intercept form.

$\left(0 , −2\right)$ and $\left(−5 , −3\right)$

Find the equation of a line containing the given points. Write the equation in slope–intercept form.

$\left(4 , 2\right)$ and $\left(4 , −3\right)$

Find the equation of a line containing the given points. Write the equation in slope–intercept form.

$\left(−2 , 1\right)$ and $\left(−2 , −4\right)$

Find the equation of a line containing the given points. Write the equation in slope–intercept form.

$\left(6 , 2\right)$ and $\left(−3 , 2\right)$

Find the equation of a line containing the given points. Write the equation in slope–intercept form.

$\left(−6 , −3\right)$ and $\left(−1 , −3\right)$

Find the equation of a line containing the given points. Write the equation in slope–intercept form.

$\left(0 , 0\right)$ and $\left(1 , 4\right)$

Find the equation of a line containing the given points. Write the equation in slope–intercept form.

$\left(−3 , 0\right)$ and $\left(−7 , −2\right)$

Find the equation of a line containing the given points. Write the equation in slope–intercept form.

$\left(3 , 5\right)$ and $\left(−7 , 5\right)$

Find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form.

line $y = 3 x + 4$, point $\left(2 , 5\right)$

Find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form.

line $y = −3 x - 1$, point $\left(2 , −3\right)$

Find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form.

line $2 x - y = 6$, point $\left(3 , 0\right)$

Find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form.

line $2 x + 3 y = 6$, point $\left(0 , 5\right)$

Find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form.

line $x = −4$, point $\left(−3 , −5\right)$

Find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form.

line $x - 6 = 0$, point $\left(4 , −3\right)$

Find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form.

line $y = 1$, point $\left(3 , −4\right)$

Find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form.

line $y + 7 = 0$, point $\left(1 , −1\right)$

Find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope–intercept form.

line $y = − x + 5$, point $\left(3 , 3\right)$

Find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope–intercept form.

line $y = \frac{2}{3} x - 4$, point $\left(2 , −4\right)$

Find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope–intercept form.

line $4 x - 3 y = 5$, point $\left(−3 , 2\right)$

Find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope–intercept form.

line $4 x + 5 y = −3$, point $\left(0 , 0\right)$

Find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope–intercept form.

line $y - 6 = 0$, point $\left(−5 , −3\right)$

Find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope–intercept form.

line y-axis, point $\left(2 , 1\right)$

Find the equation of each line. Write the equation in slope–intercept form.

Containing the points $\left(2 , 7\right)$ and $\left(3 , 8\right)$

Find the equation of each line. Write the equation in slope–intercept form.

$m = \frac{5}{6}$, containing point $\left(6 , 7\right)$

Find the equation of each line. Write the equation in slope–intercept form.

Parallel to the line $2 x + 3 y = 6$, containing point $\left(0 , 5\right)$

Find the equation of each line. Write the equation in slope–intercept form.

$m = - \frac{3}{5}$, containing point $\left(10 , −5\right)$

Find the equation of each line. Write the equation in slope–intercept form.

Perpendicular to the line y-axis, point $\left(−6 , 2\right)$

Find the equation of each line. Write the equation in slope–intercept form.

Containing the points $\left(−2 , 0\right)$ and $\left(−3 , −2\right)$

Find the equation of each line. Write the equation in slope–intercept form.

Parallel to the line $x = −4$, containing point $\left(−3 , −5\right)$

Find the equation of each line. Write the equation in slope–intercept form.

Containing the points $\left(−5 , −3\right)$ and $\left(4 , −6\right)$

Find the equation of each line. Write the equation in slope–intercept form.

Perpendicular to the line $4 x + 3 y = 1$, containing point $\left(0 , 0\right)$

Fuel consumption. The city mpg, $x$, and highway mpg, $y$, of two cars are given by the points $\left(29 , 40\right)$ and$\left(19 , 28\right)$. Find a linear equation that models the relationship between city mpg and highway mpg.

Explain in your own words why the slopes of two perpendicular lines must have opposite signs.