Question

May you write a equation of a line that is parallel to the line 4x - 2y = 8 and passes through (-2, 3)?

Answer 1

For 2 lines to be parallel, they must have the same slope. To find the slope of the lines, write the given equation in slope intercept form, you do it by solving the equation for y.

`\begin{gathered} 4x-2y=8 \\ -2y=-4x+8 \\ y=2x-4 \end{gathered}`

According to the slope intercept form equation, the slope of the lines is 2.

Now, using the slope and the given point (-2, 3), find the equation of the line by using also the point slope formula:

`\begin{gathered} y-y1=m(x-x1) \\ y-3=2(x-(-2)) \\ y=2x+4+3 \\ y=2x+7 \end{gathered}`

The equation of the line that is parallel to the line 4x-2y=8 and passes through (-2, 3) is y=2x+7.