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:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m=\dfrac{5-3}{3-(-3)}$

$m=\dfrac{2}{6}$

$m=\dfrac{1}{3}$

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:

$y-3=\dfrac{1}{3}(x-(-3))$

$y-3=\dfrac{1}{3}(x+3)$

The point slope form of the given line is $y-3=\dfrac{1}{3}(x+3)$.

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:

$y-3=\dfrac{1}{3}(x)+\dfrac{1}{3}(3)$

$y-3=\dfrac{1}{3}(x)+1$

$y=\dfrac{1}{3}(x)+1+3$

$y=\dfrac{1}{3}(x)+4$

Therefore, the slope intercept form of the given line is $y=\dfrac{1}{3}(x)+4$.