Answer:
[tex]y = \frac{1}{3}x -1[/tex]
Explanation:
Given
Parallel to: [tex]-x + 3y = -0.5[/tex]
Passes through (-9,-4)
Required
Determine the line equation
First, we calculate the slope (m) of the said line
[tex]-x + 3y = -0.5[/tex]
Make y the subject
[tex]3y = x - 0.5[/tex]
Divide through by 3
[tex]y = \frac{1}{3}x - \frac{0.5}{3}[/tex]
An equation has the general form:
[tex]y = mx + b[/tex]
Where
[tex]m = slope[/tex]
So:
[tex]m = \frac{1}{3}[/tex]
Because the required line is parallel to [tex]-x + 3y = -0.5[/tex], then they have the same slope of [tex]m = \frac{1}{3}[/tex]
Next, is to calculate the line equation using:
[tex]y = m(x - x_1) + y_1[/tex]
Where
[tex]m = \frac{1}{3}[/tex]
[tex](x_1,y_1) = (-9,-4)[/tex]
This gives:
[tex]y = \frac{1}{3}(x -(-9)) + (-4)[/tex]
[tex]y = \frac{1}{3}(x +9) -4[/tex]
Open bracket
[tex]y = \frac{1}{3}x +3 -4[/tex]
[tex]y = \frac{1}{3}x -1[/tex]
