Chapter 2.6, Problem 59E

To determine

Tofind:The slope − intercept form of equation through given points and to graph the line.

Answer to Problem 59E

The slope intercept form of the line passing through points $\left(3,2\right)$ and $\left(0,-1\right)$ is $y=x-1$ .

The graph of line $y=x-1$ is shown in Figure-1.

Explanation of Solution

Given information:

The required line passes through points $\left(3,2\right)$ and $\left(0,-1\right)$ . If slope-intercept form is not possible then explain why and use general form.

Conceptused:

The slope intercept form of the line is $y=mx+c$ , where m is the slope of the line and c the intercept made by the line on y -axis.

Calculations:

Suppose the slope-intercept form of the line passing through points $\left(3,2\right)$ and $\left(0,-1\right)$ is

  $y=mx+c$    … (1)

The point $\left(3,2\right)$ is on the line (1) so it must satisfy the equation $y=mx+c$

  $2=m\cdot 3+c$

  $\Rightarrow 3m+c=2$    … (2)

The point $\left(0,-1\right)$ is on the line (1) so it must satisfy the equation $y=mx+c$

  $-1=m\cdot 0+c$ .

  $\Rightarrow c=-1$      … (3)

From result (3) substituting value of c in result (2)

  $\Rightarrow 3m+\left(-1\right)=2$

  $\Rightarrow 3m=3$

  $\Rightarrow m=1$      … (4)

Now, substituting values of m and c in result (1)

  $y=1\cdot x-1$

  $\Rightarrow y=x-1$

Thus, the slope intercept form of the line passing through points $\left(3,2\right)$ and $\left(0,-1\right)$ is $y=x-1$ .

The graph of line $y=x-1$ is shown in Figure-1 here.

  

Conclusion:

The slope intercept form of the line passing through points $\left(3,2\right)$ and $\left(0,-1\right)$ is $y=x-1$ .

The graph of line $y=x-1$ is shown in Figure-1.