Chapter 4.1, Problem 33PPS

To determine

To find: The equation of the straight line in slope-intercept form which passes through the points $\left(5,1\right)$ and $\left(0,4\right)$ as shown in graph

  

Answer to Problem 33PPS

The equation of straight line in slope-intercept form is $y=-\frac{3}{5}x+4$ .

Explanation of Solution

Given information:From the given graph of the line, the line passes through the points $\left(5,1\right)$ and $\left(0,4\right)$ . And, the line has y-intercept equal to 4 as shown in graph.

Calculation: Using the points $\left(5,1\right)$ and $\left(0,4\right)$ , the slope of the line is calculated as

  $\begin{array}{c}m=\frac{4-1}{0-5}\left(\begin{array}{l}\text{Using formula for}\\ \text{slope}\left(m\right)=\frac{y_2-y_1}{x_2-x_1}\end{array}\right)\\ =-\frac{3}{5}\mathrm{......}\left(1\right)\end{array}$

Now equation of the straight line using the slope intercept form $y=mx+c$ , where $m$ is the slope of the line and $c$ is y-intercept of the given line is written as,

  $y=-\frac{3}{5}x+4$