Question

Find the equation of the line through the points (-3,3) and (3,5) using point-slope form. Then rewrite the equation in slope-intercept form.

Answer 1

Given:

A line passes through the points (-3,3) and (3,5).

To find:

The equation of the line by using point slope form, then rewrite the equation in slope-intercept form.

Solution:

It is given that the line passes through the points (-3,3) and (3,5). So, the slope of the line is:

`m=(y_2-y_1)/(x_2-x_1)`

`m=(5-3)/(3-(-3))`

`m=(2)/(6)`

`m=(1)/(3)`

The point slope form of a line is:

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

Where, m is the slope.

The point slope form of the given line is:

`y-3=(1)/(3)(x-(-3))`

`y-3=(1)/(3)(x+3)`

The point slope form of the given line is
`y-3=(1)/(3)(x+3)`.

We need to rewrite this equation in slope intercept form, i.e.,
`y=mx+b`, where m is slope and b is y-intercept.

The above equation can be rewritten as:

`y-3=(1)/(3)(x)+(1)/(3)(3)`

`y-3=(1)/(3)(x)+1`

`y=(1)/(3)(x)+1+3`

`y=(1)/(3)(x)+4`

Therefore, the slope intercept form of the given line is
`y=(1)/(3)(x)+4`.