Answer:
The equation of the line is:
- [tex]y=\frac{1}{4}x+\frac{37}{4}[/tex]
Step-by-step explanation:
Given the points
Finding the slope between the points
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-5,\:8\right),\:\left(x_2,\:y_2\right)=\left(-1,\:9\right)[/tex]
[tex]m=\frac{9-8}{-1-\left(-5\right)}[/tex]
[tex]m=\frac{1}{4}[/tex]
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
substituting the values m = 1/4 and the point (-5, 8)
[tex]y-8=\frac{1}{4}\left(x-\left(-5\right)\right)[/tex]
[tex]y-8=\frac{1}{4}\left(x+5\right)[/tex]
Add 8 to both sides
[tex]y-8+8=\frac{1}{4}\left(x+5\right)+8[/tex]
[tex]y=\frac{1}{4}x+\frac{37}{4}[/tex]
Thus, the equation of the line is:
- [tex]y=\frac{1}{4}x+\frac{37}{4}[/tex]
