Chapter 8.8, Problem 60MR

To determine

Tograph:The given equation using slope and y - intercept.

Explanation of Solution

Given information:

The equation to graph is $y=2x-3$ .

Formulaused:

The equation $y=mx+c$ represents a line with slope m and y -intercept c.

  

The slope of line is equal $\theta$

  $m=\tan \theta =\frac{OA}{OB}$

  $\Rightarrow OB=\frac{OA}{m}=\frac{c}{m}$ . Thus, point B can be obtained.

Graph:

The given equation of line is $y=2x-3$  ... (1)

Comparing equation (1) with equation $y=mx+c$ , we have $m=2$ and $c=-3$ .

Thus, the required line passes through point $A\left(0,c\right)=A\left(0,-3\right)$ .

The point B can be obtained by formula $OB=\frac{3}{2}=1.5$ .

Thus, another point on the line is $B\left(OB,0\right)=B\left(1.5,0\right)$ .

The line joining points $A\left(0,-3\right)$ and $B\left(1.5,0\right)$ is the required line $y=2x-3$ for which graph is shown in Figure-1.

  

Interpretation.

The line $y=2x-3$ makes angle $\theta$ with x -axis such that $\tan \theta =-\frac{OA}{OB}=-\frac{-3}{3/2}=2$ .