Question

Find the equation of a line that is parallel to the graph of y-3x=4 and has the same y-intercept as the graph of 4y+x=36

Answer 1

The slope intercept form of a line is given by:

`\begin{gathered} y=mx+b \\ where \\ m=slope \\ b=y-intercept \end{gathered}`

Two lines are parallel if:

`m1=m2`

Where:

m1 = slope of the line 1

m2 = slope of the line 2

Rewrite the equations in the slope intercept form:

`\begin{gathered} y-3x=4 \\ y=3x+4 \end{gathered}`

From the previous equation we can conclude that the slope is m = 3, since the line we need to find is parallel to this one, we can conclude that the slope of the line we are trying to find is also m = 3

For the other equation:

`\begin{gathered} 4y+x=36 \\ 4y=36-x \\ y=-(1)/(4)x+9 \end{gathered}`

From this line we can conclude that the y-intercept is b = 9, since the line we are trying to find has the same y-intercept, we can conclude that its y-intercept is also b = 9. Therefore, the equation of the line is:

`y=3x+9`