Question

Use the point-slope form of a line to write the equation of

a line that has a slope of 2 and passes through the point
(4,3). Write the equation in slope-intercept form.

Answer 1

y=2x-5

Explanation:

Hi there!

We are given that a line has a slope of 2, and passes through the point (4,3)

We want to use point-slope form to find this equation of the line, yet we want to write this in 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

As we are already given the slope and a point, we can substitute these values into the formula to find the line.

First, substitute 2 as m in the equation:

`y-y_1=2(x-x_1)`

Now substitute 4 as
`x_1` and 3 as
`y_1`

`y-3=2(x-4)`

This is the equation of the line in point-slope form.

Now we need to write it in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

We can actually get to slope-intercept form from point-slope form.

First, distribute 2 to both x and -4 on the right side

y-3=2x-8

Now add 3 to both sides

y=2x-5

Hope this helps!