Question

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

Answer 1

`\displaystyle y=(3)/(5)x-2`

Explanation:

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

`\displaystyle y=(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)=(3)/(5)(x-(-5))`

Simplify:

`\displaystyle y+5=(3)/(5)(x+5)`

Distribute:

`\displaystyle y+5=(3)/(5)x+3`

Subtract 5 from both sides:

`\displaystyle y=(3)/(5)x-2`

And we have our equation.