Chapter 5.4, Problem 11P

Write an equation in point-slope form of the line through the given points. Then write the equation in slope-intercept form.

$(4,0),(-2,1)$

To determine

To find: The equation that passes through $(4,0)$ and $(-2,1)$ .

Answer to Problem 11P

The point-slope form is $y=-\frac{1}{6}(x-4)$

The slope-intercept form is $y=-\frac{1}{6}x+\frac{2}{3}$ .

Explanation of Solution

Given information:

The points are $(4,0),(-2,1)$

From the given points, the slope of the line is

  $\begin{array}{l}m=\frac{\Delta y}{\Delta x}=\frac{1-0}{-2-4}\\ \Rightarrow m=\frac{1}{-6}=-\frac{1}{6}\end{array}$

Therefore, the equation of the line in point-slope form would be

  $\begin{array}{l}y-0=-\frac{1}{6}(x-4)\\ \Rightarrow y=-\frac{1}{6}(x-4)\end{array}$

Rewriting this in the slope-intercept form would be

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

Conclusion:

The point-slope form is $y=-\frac{1}{6}(x-4)$

The slope-intercept form is $y=-\frac{1}{6}x+\frac{2}{3}$ .