Question

What is an equation of the line that passes through the point (2,2) and is parallel to the line x – 2y = 4?

Answer 1

Two lines that are parallel have the same slope.

In this case, the slope of the parallel line has to be calcaulted, as it is not expressed in slope-intercept form:

`\begin{gathered} x-2y=4 \\ x-4=2y \\ (x-4)/(2)=y \\ y=(1)/(2)x-2 \end{gathered}`

The slope is the coefficient of x, so it is m=1/2.

As we know the slope, we can find the y-intercept of our line by replacing in the equation the known point (2,2):

`\begin{gathered} y=(1)/(2)x+b \\ 2=(1)/(2)\cdot2+b \\ 2=1+b \\ b=2-1 \\ b=1 \end{gathered}`

The equation of the line is:

`y=(1)/(2)x+1`

Answer: y=(1/2)*x+1