Question

Write an equation in slope - intercept form for the line that passes through the given paint andis parallel to the given equation.(9, 12), y = 13x-4

Answer 1

The equation of a line is given by

`y-y_1=m(x-x_1)`

where m is the slope of the line and (x1,y1) is a point where the line passes through.

In our case we have a point but we don't have the slope yet, so we have to find it. To do this we have to remember that two lines are parallel if and only if their slopes are equal, that is

`m_1=m_2`

We know that the line we are looking for is parallel to the line

`y=13x-4`

we notice that this line in written in the slope-intercept form

`y=mx+b`

then its slope is 13.

Since the line is parallel to the one we are looking for, our slope is also 13.

Using the point (9,12) and the slope the equation of the line is

`y-12=13(x-9)`

now we have to write in the slope-intercept form

`\begin{gathered} y-12=13x-117 \\ y=13x-117+12 \\ y=13x-115 \end{gathered}`

Therefore the line is

`y=13x-115`