a line passes through the points (-5, -8) and (3, 6). write its equation in slope - intercept form. write…

Explanation:

Step1: Calculate the slope (m)

The slope formula is (m=\frac{y_2 - y_1}{x_2 - x_1}). Given ((x_1,y_1)=(-5,-8)) and ((x_2,y_2)=(3,6)), then (m=\frac{6-(-8)}{3 - (-5)}=\frac{6 + 8}{3+5}=\frac{14}{8}=\frac{7}{4}).

Step2: Use the point - slope form to find the (y) - intercept (b)

The point - slope form is (y=mx + b). We can use the point ((3,6)) and (m = \frac{7}{4}). Substitute into the equation: (6=\frac{7}{4}\times3 + b). Then (6=\frac{21}{4}+b). Solve for (b): (b=6-\frac{21}{4}=\frac{24 - 21}{4}=\frac{3}{4}).

Answer:

(y=\frac{7}{4}x+\frac{3}{4})