Chapter 5.3, Problem 21P

Write an equation in slope-intercept form of the line that passes through the given points.

$(-1,3)$ and $(-3,1)$

To determine

To find: The equation in slope-intercept form of the line that passes through $(-1,3)$ and $(-3,1)$ .

Answer to Problem 21P

The equation of the line is $y=x+4$ .

Explanation of Solution

Given information:

The points are $(-1,3)$ and $(-3,1)$ .

Formula used:

Slope-intercept form: $y=mx+b$ , where $m$ represents the slope and $b$ represents the y -intercept.

From the given points, the slope of the line would be

  $\frac{1-3}{-3-(-1)}=\frac{-2}{-2}=1$

Since the slope is $m=1$ , the equation of the line would be $y=x+b$ .

To find $b$ : Since the line passes through the point $(-1,3)$ , it must satisfies $y=x+b$ .

  $\begin{array}{l}3=-1+b\\ \Rightarrow b=3+1=4\end{array}$

Conclusion:

Therefore, the equation of the line is $y=x+4$ .