Question

Find the equation of a line that is parallel to y = 5x + 1 and passes through the point (3, -4).

Give your answer in the form y = mx + b.

Answer 1

Given:

The equation of a line is:

`y=5x+1`

A line is parallel to the given line and passes through the point (3,-4).

To find:

The equation of the line in the slope intercept form.

Solution:

The slope intercept form of a line is:

`y=mx+b` ...(i)

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

We have,

`y=5x+1` ...(ii)

On comparing (i) and (ii), we get

`m=5`

Slope of the given line is 5.

We know that the slopes of parallel lines are equal. So, the slope of the required line is 5.

The required line passes through the point (3,-4) with slope 5. So, the equation of the required line is:

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

`y-(-4)=5(x-3)`

`y+4=5(x)+5(-3)`

`y+4=5x-15`

Subtracting 4 from both sides, we get

`y+4-4=5x-15-4`

`y=5x-19`

Therefore, the equation of the required line is
`y=5x-19`.