Chapter 3, Problem 1RP

Graph the straight line determined by each of the following equations.

$y=-\frac{3}{2}x+5$

To determine

To graph: The equation of the straight line $y=-\frac{3}{2}x+5$.

Explanation of Solution

Given:

The equation of the straight line is $y=-\frac{3}{2}x+5$.

Graph:

Since, $y=-\frac{3}{2}x+5$

Put $x=0$;

$\begin{array}{c}y=-\frac{3}{2}\left(0\right)+5\\ =5\end{array}$

Put $x=2$;

$\begin{array}{c}y=-\frac{3}{2}\left(2\right)+5\\ =-3+5\\ =2\end{array}$

Put $x=4$;

$\begin{array}{c}y=-\frac{3}{2}\left(4\right)+5\\ =-6+5\\ =-1\end{array}$

Put $x=\frac{10}{3}$;

$\begin{array}{c}y=-\frac{3}{2}\left(\frac{10}{3}\right)+5\\ =-5+5\\ =0\end{array}$

Use the following points to plot the graph;

x	0	$\frac{10}{3}$	2	4
y	$5$	0	$2$	$-1$

Plot the points on graph and connect the points with a straight line.

Hence, the graph is obtained as follows;

Interpretation:

The slop of the straight line is negative.