Answer:
An equation in point-slope form of the line that passes through (-4,1) and (4,3) will be:
[tex]y-1=\frac{1}{4}\left(x+4\right)[/tex]
Step-by-step explanation:
Given the points
Finding the slope between the points (-4,1) and (4,3)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-4,\:1\right),\:\left(x_2,\:y_2\right)=\left(4,\:3\right)[/tex]
[tex]m=\frac{3-1}{4-\left(-4\right)}[/tex]
Refine
[tex]m=\frac{1}{4}[/tex]
Point slope form:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where
in our case,
substituting the values m = 1/4 and the point (-4,1) in the point slope form of line equation.
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-1=\frac{1}{4}\left(x-\left(-4\right)\right)[/tex]
[tex]y-1=\frac{1}{4}\left(x+4\right)[/tex]
Thus, an equation in point-slope form of the line that passes through (-4,1) and (4,3) will be:
[tex]y-1=\frac{1}{4}\left(x+4\right)[/tex]
