Chapter 5.3, Problem 27P

Write an equation in slope-intercept form of the line that passes through the given points. (2,8) and (-3,6)

To determine

To find: The equation in slope-intercept form of the line that passes through $(2,8)$ and $(-3,6)$ .

Answer to Problem 27P

The equation of the line is $y=\frac{2}{5}x+\frac{36}{5}$ .

Explanation of Solution

Given information:

The points are $(2,8)$ and $(-3,6)$ .

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

  $\frac{6-8}{-3-2}=\frac{-2}{-5}=\frac{2}{5}$

Since the slope is $m=\frac{2}{5}$ , the equation of the line would be $y=\frac{2}{5}x+b$ .

To find $b$ : Since the line passes through the point $(2,8)$ , it must satisfies $y=\frac{2}{5}x+b$ .

  $\begin{array}{l}8=\frac{2}{5}(2)+b\\ \Rightarrow 8=\frac{4}{5}+b\\ \Rightarrow b=8-\frac{4}{5}=\frac{40-4}{5}\\ \Rightarrow b=\frac{36}{5}\end{array}$

Conclusion:

Therefore, the equation of the line is $y=\frac{2}{5}x+\frac{36}{5}$ .