Chapter 4.1, Problem 37PPS

To determine

To find: The equation of line in slope intercept form that passes through points $\left(\frac{5}{12},-1\right)$ and $\left(-\frac{3}{4},\frac{1}{6}\right)$ .

Answer to Problem 37PPS

The equation of line passes through points $\left(\frac{5}{12},-1\right)$ and $\left(-\frac{3}{4},\frac{1}{6}\right)$ is $y=-x-\frac{7}{12}$ .

Explanation of Solution

Given:

The line passes through the points $\left(\frac{5}{12},-1\right)$ and $\left(-\frac{3}{4},\frac{1}{6}\right)$ .

Concept used:

The formula for the slope of the line $m$ containing points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is:

$m=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

Replace $\left(x_1,y_1\right)$ as $\left(\frac{5}{12},-1\right)$ and $\left(x_2,y_2\right)$ as $\left(-\frac{3}{4},\frac{1}{6}\right)$ in the slope formula $m=\frac{y_2-y_1}{x_2-x_1}$ as:

$\begin{array}{c}m=\frac{-1-\frac{1}{6}}{\frac{5}{12}-\left(-\frac{3}{4}\right)}\\ =\frac{-\frac{7}{6}}{\frac{7}{6}}\\ =-1\end{array}$

The intercept for the equation of the line with slope $-1$ and point $\left(\frac{5}{12},-1\right)$ is calculated as,

$\begin{array}{c}-1=-1\left(\frac{5}{12}\right)+b\\ -1+\frac{5}{12}=b\\ -\frac{7}{12}=b\end{array}$

Substitute $m=-1$ , $b=-\frac{7}{12}$ in equation $y=mx+b$ to obtain equation of line.

$y=-x-\frac{7}{12}$

Therefore, the equation of line passes through points $\left(\frac{5}{12},-1\right)$ and $\left(-\frac{3}{4},\frac{1}{6}\right)$ is $y=-x-\frac{7}{12}$ .