Answer:
The equation of the line is:
[tex]y=\frac{2}{5}x+1[/tex]
Step-by-step explanation:
Given the points
Finding the slope between points
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-5,\:-1\right),\:\left(x_2,\:y_2\right)=\left(5,\:3\right)[/tex]
[tex]m=\frac{3-\left(-1\right)}{5-\left(-5\right)}[/tex]
[tex]m=\frac{2}{5}[/tex]
Using the point-slope form to find the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
substituting the values m = 2/5 and the point (5, 3)
[tex]y-3=\frac{2}{5}\left(x-5\right)[/tex]
Add 3 to both sides
[tex]y-3+3=\frac{2}{5}\left(x-5\right)+3[/tex]
[tex]y=\frac{2}{5}x+1[/tex]
Thus, the equation of the line is:
[tex]y=\frac{2}{5}x+1[/tex]
