Question

Find an equation of a line parallel to the line that contains the given point. Write the equation in slope-intercept form Line 4x-y=9, point (2,5)

Answer 1

A line equation can be written in slope-intercept form, which is

`y=mx+b`

where m represents the slope and b represents the y-intercept.

Parallel lines have the same slope. If we rewrite the given line equation in slope-intercept form and identify the slope, it will be the same slope of our line.

Rewritting the given line equation, we have

`\begin{gathered} 4x-y=9 \\ -y=-4x+9 \\ y=4x-9 \end{gathered}`

The slope of the given line is equal to 4. Our line equation is

`y=4x+b`

To identify the y-intercept, we can evaluate the given point that belongs to this line.

Evaluating the point, we have

`\begin{gathered} (5)=4(2)+b \\ 5=8+b \\ b=5-8 \\ b=-3 \end{gathered}`

The equation of our line is

`y=4x-3`