The equation of a line in point-slope form is:
y - y1 = m(x - x1)
The slope m of a line is given by the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]In this case, we are given the points (4,8) and (-9,5), then we get:
[tex]m=\frac{5-8}{-9-4}=\frac{-3}{-13}=\frac{3}{13}[/tex]By replacing the value of m into the point-slope equation, we get:
[tex]y-y1=\frac{3}{13}(x-x1)[/tex]By replacing 4 for x1 and 8 for y1, we get:
[tex]y-8=\frac{3}{13}(x-4)[/tex]