Answer:
[tex]y = \frac{2}{5} x - 7 \frac{3}{5} [/tex]
Step-by-step explanation:
Slope-intercept form
y= mx +c, where m is the gradient and c is the y-intercept.
[tex]\boxed{gradient = \frac{y1 - y2}{x1 - x2} }[/tex]
Gradient
[tex] = \frac{ - 4 - ( - 8)}{9 - ( - 1)} [/tex]
[tex] = \frac{ - 4 + 8}{9 + 1} [/tex]
[tex] = \frac{4}{10} [/tex]
[tex] = \frac{2}{5} [/tex]
Substitute the value of the gradient into the equation:
[tex]y = \frac{2}{5} x + c[/tex]
To find the value of the y-intercept, substitute a pair of coordinates.
When x= -1, y= -8,
[tex] - 8 = \frac{2}{5} ( - 1) + c[/tex]
[tex] - 8 = - \frac{2}{5} + c[/tex]
[tex]c = - 8 + \frac{2}{5} [/tex]
[tex]c = - 7 \frac{3}{5} [/tex]
Thus the equation of the line is [tex]y = \frac{2}{5} x - 7 \frac{3}{5} [/tex].
