Answer:
[tex]\displaystyle y=-\frac{2}{3}x+3[/tex]
Step-by-step explanation:
We want to find the equation of the line that is parallel to:
[tex]\displaystyle y=-\frac{2}{3}x[/tex]
And passes through (-3,5).
First, we need to determine the slope of our new line.
Remember that parallel lines have the same slope.
Since the slope of our original line is -2/3, this means that the slope of our new line must also be -2/3.
Now, we can use the point-slope form given by:
[tex]y-y_1=m(x-x_1)[/tex]
We will let (-3, 5) be (x₁, y₁). By substitution:
[tex]\displaystyle y-(5)=-\frac{2}{3}(x-(-3))[/tex]
Simplify:
[tex]\displaystyle y-5=-\frac{2}{3}(x+3)[/tex]
Distribute:
[tex]\displaystyle y-5=-\frac{2}{3}x-2[/tex]
Add 5 to both sides. So, our equation is:
[tex]\displaystyle y=-\frac{2}{3}x+3[/tex]
