Question

Write an equation of a line that passes through the point (-5,5) and is parallel to the line y=(-3/5)x-3

Answer 1

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

Explanation:

We want to wite the equation of a line that is parallel to:

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

And passes through the point (-5, 5).

First, remember that parallel lines have the same slope.

Therefore, since the slope of the original line is -3/5, the slope of our new line is also -3/5.

Now, we can use the point-slope form:

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

Where m is the slope and (x₁, y₁) is a point.

So, we will substitute -3/5 for m and (-5, 5) for (x₁, y₁). This yields:

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

Simplify:

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

Distribute:

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

Add 5 to both sides. Hence, our equation is:

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