Answer:
[tex]y =- \frac{5}{13}x - \frac{1}{13}[/tex]
Step-by-step explanation:
First, calculate the slope using the slope formula and the two points given.
[tex]m = \frac{y_2-y_1}{x_2-x_1}= \frac{3--2}{-8-5} =-\frac{5}{13}[/tex]
Write the equation of the line using m = -5/13 and the point (5,-2) into the point slope form. Then simplify into the slope intercept form.
[tex]y - y_1=m(x-x_1)\\y - -2 = -\frac{5}{13}(x-5)\\y+2 =- \frac{5}{13}x +\frac{25}{13}\\y =- \frac{5}{13}x - \frac{1}{13}[/tex]
