Question

Find the distance between the parallel line y = 2x + 7 y = 2x - 2

Answer 1

A line is represented by the following expression:

`\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}`

Since they are parallel because they have the same slope, we can find the distance between them with the formula for distance between points:

`\begin{gathered} y=2x+7 \\ y=2(1)+7 \\ y=9 \\ \text{Point for the first line (1,9)} \\ \\ y=2x-2 \\ y=2(1)-2 \\ y=0 \\ \text{Point for the second line (1,0)} \end{gathered}`

Distance between points is represented by the following expression:

`d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)}^2`
`\begin{gathered} d=\sqrt[]{(1-1)^2+(9-0)^2} \\ d=\sqrt[]{9^2} \\ d=9\text{ units} \end{gathered}`

The distance between the lines is 9 units.