Chapter 4.1, Problem 36PPS

To determine

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

Answer to Problem 36PPS

The equation of line passes through points $\left(\frac{5}{4},1\right)$ and $\left(-\frac{1}{4},\frac{3}{4}\right)$ is $y=\frac{1}{6}x+\frac{19}{24}$ .

Explanation of Solution

Given:

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

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

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

The intercept for the equation of the line with slope $\frac{1}{6}$ and point $\left(\frac{5}{4},1\right)$ is calculated as,

$\begin{array}{c}1=\frac{1}{6}\left(\frac{5}{4}\right)+b\\ 1-\frac{5}{24}=b\\ \frac{19}{24}=b\end{array}$

Substitute $m=\frac{1}{6}$ , $b=\frac{19}{24}$ in equation $y=mx+b$ to obtain equation of line.

$y=\frac{1}{6}x+\frac{19}{24}$

Therefore, the equation of line passes through points $\left(\frac{5}{4},1\right)$ and $\left(-\frac{1}{4},\frac{3}{4}\right)$ is $y=\frac{1}{6}x+\frac{19}{24}$ .