Question

Write an equation for line L in point-slope form and slope-intercept form.

L is parallel to y=5x

Answer 1

Point-slope form:
`y+4=5(x-2)`
Slope-intercept form:
`y=5x-14`

Explanation:

Pre-Solving

We are given that one line has the equation y = 5x.

We also know that another line, L is parallel to y=5x and passes through the point (2, -4).

We want to write the equation of L in both point-slope form and slope-intercept form.

Point-slope form is given as
`y-y_1=m(x-x_1)`, where m is the slope and
`(x_1, y_1)` is a point.

Slope-intercept form is y=mx+b, where m is the slope and b is the value of y at the y-intercept.

Also recall that parallel lines have the same slope.

Solving

Slope

First, we can find the slope of y=5x.

Notice how the line is in slope-intercept form, and that the coefficient of 5 is m in mx.

Therefore, the slope of y=5x is 5.

It is also the slope of line L.

Point-Slope Form

We can start with writing the equation of line L in point-slope form.

We can start by substituting 5 as m in
`y-y_1=m(x-x_1)`.

We get:

`y-y_1=5(x-x_1)`

Now substitute 2 as
`x_1` and -4 as
`y_1`.

`y--4=5(x-2)`

We can simplify this to:

`y+4=5(x-2)`

Slope-Intercept Form

Now we can write the equation of line L in slope-intercept form.

We can take the point-slope form and turn it into slope-intercept form.

Start by distributing 5 to both x and -2 on the right side.

We get:

y + 4 = 5x - 10

Now, subtract 4 from both sides.

y = 5x - 14