Question

Write the equation of the line that passes through the points −6,1) and (1,2). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Answer 1

Hi there! I'll help you solve this problem!

We are asked to find the equation of the line when we're given the following two points:

• (-6,1) and (1,2)

First we'll find the slope of the line using the slope formula.

`\sf{m=\cfrac{y_2-y_1}{x_2-x_1}}`

Substitute the data:

`\sf{m=\cfrac{2-1}{1-(-6)}}`

`\sf{m=\cfrac{1}{1+6}}`

`\sf{m=\cfrac{1}{7}}`

Therefore the slope is 1/7.

Now we'll take the first point and substitute the slope and the point into the point-slope formula:

`\large\boldsymbol{\sf{y-y_1=m(x-x_1)}}`

`\boldsymbol{\sf{y-1=\cfrac{1}{7}(x-(-6)}}`

Simplify:

`\boldsymbol{\sf{y-1=\cfrac{1}{7}(x+6)}}`

Therefore, this is our point slope equation.

`\dotfill`

Best wishes!