Question

Through: (-5, -5), parallel to y = 3/5x + 3

Answer 1

Answer:

$\displaystyle y=\frac{3}{5}x-2$

Step-by-step explanation:

We want to find the equation of a line parallel to:

$\displaystyle y=\frac{3}{5}x+3$

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:

$y-y_1=m(x-x_1)$

We will let (-5, -5) be (x₁, y₁). m is the slope or 3/5. Hence:

$\displaystyle y-(-5)=\frac{3}{5}(x-(-5))$

Simplify:

$\displaystyle y+5=\frac{3}{5}(x+5)$

Distribute:

$\displaystyle y+5=\frac{3}{5}x+3$

Subtract 5 from both sides:

$\displaystyle y=\frac{3}{5}x-2$

And we have our equation.