Question

8. Write the slope-intercept form of the equation of theline through (2, 2) and parallel to y = x + 4.

Answer 1

y = x

Step-by-step explanation:

The slope-intercept form of the equation of a line is generally given as;

`y=mx+b`

where m = slope of the line

b = y-intercept of the line

Given the line;

`y=x+4`

We can see that the slope(m) = 1.

Note that the slopes of parallel lines are equal, therefore the slope of the line parallel to y = x + 4 will also be 1.

Let's go ahead and determine the y-intercept of the parallel line using the point (2, 2) and slope(m) = 1;

`\begin{gathered} y=mx+b \\ 2=(1)(2)+b \\ b=2-2 \\ b=0 \end{gathered}`

Having b = 0 and m = 1, the slope-intercept form of the equation of the parallel line can be written as y = x.