Question

Write an equation in slope-intercept form of a line passingthrough the given point and parallel to the given line1. (2, 1); y = 5x - 6

Answer 1

DEFINITION

The equation of a linear graph in the slope-intercept form is given to be:

`y=mx+b`

where m is the slope of the line and b is the y-intercept.

If two lines are parallel, this means that the slopes of both lines are equal.

SOLUTION

The line is said to be parallel with the line:

`y=5x-6`

Since the slope is 5, the slope of the required graph is 5 as well and thus, we have the equation of the line looking as follows:

`y=5x+b`

We can calculate the value of b by substituting any point on the graph into the equation. Given the point (2, 1), we have:

`\begin{gathered} (x,y)=(2,1) \\ \therefore \\ 1=5(2)+b \\ 1=10+b \\ b=1-10 \\ b=-9 \end{gathered}`

Therefore, the equation of the line is given to be:

`y=5x-9`