Answer:
[tex]\displaystyle y=\frac{3}{5}x-2[/tex]
Step-by-step explanation:
We want to find the equation of a line parallel to:
[tex]\displaystyle y=\frac{3}{5}x+3[/tex]
And passes through (-5, -5).
Recall that parallel lines must have the same slope.
Since the slope of our old line is 3/5, the slope of our new line must also be 3/5.
So, we know that the slope of our new line is 3/5 and it passes through (-5, -5).
Now, we can use the point-slope form given by:
[tex]y-y_1=m(x-x_1)[/tex]
We will let (-5, -5) be (x₁, y₁). m is the slope or 3/5. Hence:
[tex]\displaystyle y-(-5)=\frac{3}{5}(x-(-5))[/tex]
Simplify:
[tex]\displaystyle y+5=\frac{3}{5}(x+5)[/tex]
Distribute:
[tex]\displaystyle y+5=\frac{3}{5}x+3[/tex]
Subtract 5 from both sides:
[tex]\displaystyle y=\frac{3}{5}x-2[/tex]
And we have our equation.
