Answer:
[tex]y=-\frac{2}{3}x-\frac{10}{3}[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
1) Determine the slope (m)
[tex]y =-\frac{2}{3} x +4[/tex]
In the given equation, [tex]-\frac{2}{3}[/tex] is in the place of m, making it the slope. Because parallel lines always have the same slope, the slope of the line we're currently solving for is [tex]-\frac{2}{3}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-\frac{2}{3}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=-\frac{2}{3}x+b[/tex]
Plug in the given point (-2,-2) to solve for b
[tex]-2=-\frac{2}{3}(-2)+b\\-2=\frac{4}{3}+b[/tex]
Subtract [tex]\frac{4}{3}[/tex] from both sides to isolate b
[tex]-2-\frac{4}{3}=\frac{4}{3}+b-\frac{4}{3}\\-\frac{10}{3} =b[/tex]
Therefore, the y-intercept of the line is [tex]-\frac{10}{3}[/tex]. Plug this back into [tex]y=-\frac{2}{3}x+b[/tex]:
[tex]y=-\frac{2}{3}x-\frac{10}{3}[/tex]
I hope this helps!
