DEFINITION
The equation of a linear graph in the slope-intercept form is given to be:
[tex]y=mx+b[/tex]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:
[tex]y=5x-6[/tex]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:
[tex]y=5x+b[/tex]We can calculate the value of b by substituting any point on the graph into the equation. Given the point (2, 1), we have:
[tex]\begin{gathered} (x,y)=(2,1) \\ \therefore \\ 1=5(2)+b \\ 1=10+b \\ b=1-10 \\ b=-9 \end{gathered}[/tex]Therefore, the equation of the line is given to be:
[tex]y=5x-9[/tex]