Answer:
[tex]y = -\frac{3}{5}x -\frac{8}{5}[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (-1,-1)[/tex]
[tex](x_2,y_2) = (4,-4)[/tex]
Required
Determine the line equation
First, calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{-4 - (-1)}{4 - (-1)}[/tex]
[tex]m = \frac{-4 +1}{4 +1}[/tex]
[tex]m = \frac{-3}{5}[/tex]
[tex]m = -\frac{3}{5}[/tex]
The equation is then calculated using:
[tex]y - y_1 = m(x - x_1)[/tex]
This gives:
[tex]y - (-1) = -\frac{3}{5}(x - (-1))[/tex]
[tex]y + 1 = -\frac{3}{5}(x +1))[/tex]
Open bracket
[tex]y + 1 = -\frac{3}{5}x -\frac{3}{5}[/tex]
Make y the subject
[tex]y = -\frac{3}{5}x -\frac{3}{5}-1[/tex]
[tex]y = -\frac{3}{5}x +\frac{-3-5}{5}[/tex]
[tex]y = -\frac{3}{5}x +\frac{-8}{5}[/tex]
[tex]y = -\frac{3}{5}x -\frac{8}{5}[/tex]
