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

Answer:

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

• $y=-3x+2$

Step-by-step explanation:

Given the points

• (-2, 8) and (1, -1)

$\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

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

$m=\frac{-1-8}{1-\left(-2\right)}$

$m=-3$

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:

• $y=-3x+2$