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=(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)=(3-(-7))/(-6-6)(x-6)`

`y+7=(3+7)/(-12)(x-6)`

`y+7=(10)/(-12)(x-6)`

`y+7=-(5)/(6)(x-6)`

Using distributive property, we get

`y+7=-(5)/(6)(x)-(5)/(6)(-6)`

`y+7=-(5)/(6)x+5`

Subtract 7 from both sides.

`y=-(5)/(6)x+5-7`

`y=-(5)/(6)x-2`

Therefore, the equation of line is
`y=-(5)/(6)x-2`.