Question

What is an equation of the line that passes through the points (6, -7)(6,−7) and (-6, 3)(−6,3)? Put your answer in fully reduced form.

Answer 1

Given:

A line passes through the points (6,-7) and (-6,3).

To find:

The equation of line.

Solution:

If a line passes through two points $(x_1,y_1)\text{ and }(x_2,y_2)$, then the equation of line is

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

The line passes through the points (6,-7) and (-6,3). So, the equation of line is

$y-(-7)=\dfrac{3-(-7)}{-6-6}(x-6)$

$y+7=\dfrac{3+7}{-12}(x-6)$

$y+7=\dfrac{10}{-12}(x-6)$

$y+7=-\dfrac{5}{6}(x-6)$

Using distributive property, we get

$y+7=-\dfrac{5}{6}(x)-\dfrac{5}{6}(-6)$

$y+7=-\dfrac{5}{6}x+5$

Subtract 7 from both sides.

$y=-\dfrac{5}{6}x+5-7$

$y=-\dfrac{5}{6}x-2$

Therefore, the equation of line is $y=-\dfrac{5}{6}x-2$.