Question

What is an equation of the line that passes through the points (-2, 8) and (1,−1)? Put your answer in fully reduced form.

Answer 1

The equation of a line that passes through the points (-2, 8) and (1,−1) in the fully reduced form will be:

• 
  `y=-3x+2`

Explanation:

Given the points

• (-2, 8) and (1, -1)

`\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(-2,\:8\right),\:\left(x_2,\:y_2\right)=\left(1,\:-1\right)`

`m=(-1-8)/(1-\left(-2\right))`

`m=-3`

As the equation of a line in point-slope form is given by:

`y-y_1=m\left(x-x_1\right)`

substituting the values m = -3 and the point (-2, 8)

`y-8=-3\left(x-\left(-2\right)\right)`

`y-8=-3\left(x+2\right)`

`y-8+8=-3\left(x+2\right)+8`

`y=-3x+2`

Therefore, the equation of a line that passes through the points (-2, 8) and (1,−1) in the fully reduced form will be:

• 
  `y=-3x+2`