Question

What is the distance between parallel lines whose equations are y = 2x + 7 and y = 2x – 3?

Answer 1

Answer:

The distance is $\sqrt{20}$ or $2\sqrt{5}$.

Step-by-step explanation:

Slope of parallel: 2

Slope of perpendicular: -1/2

Pick a point for y =2x + 7. For example (0,7)

Use the perpendicular slope to get to the other line to find the other point of y=2x-3. Look at the screenshot...I got (4,5).

Distance formula $\sqrt{(x_{2}-x_{1} )^{2}+(y_{2} -y_{1})^2 }$

Insert (0,7) and (4,5)

$\sqrt{(0-4)^{2}+(7-5)^2 }$ = $\sqrt{(-4)^{2}+(2)^2 } = \sqrt{(16)+(4)} } = \sqrt{20} = 2\sqrt{5}$