Answer:
[tex]m = -\frac{1}{2}[/tex]
[tex]y\ intercept = -1[/tex]
[tex]y = -\frac{1}{2}x -1[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (-2,0)[/tex]
[tex](x_2,y_2) = (0,-1)[/tex]
Required
Determine the slope and y intercept from graph
To calculate the slope, we have:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{-1-0}{0 - (-2)}[/tex]
[tex]m = \frac{-1}{0 +2}[/tex]
[tex]m = -\frac{1}{2}[/tex]
The y intercept is when [tex]x = 0[/tex]
So,
[tex]y\ intercept = -1[/tex]
The equation is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
This gives
[tex]y = -\frac{1}{2}(x - (-2)) + 0[/tex]
[tex]y = -\frac{1}{2}(x - (-2))[/tex]
[tex]y = -\frac{1}{2}(x +2)[/tex]
[tex]y = -\frac{1}{2}x -\frac{1}{2}*2[/tex]
[tex]y = -\frac{1}{2}x -1[/tex]
See attachment for graph
