Question

What is an equation of the line that passes through the points (-6, -2) and
(-3,2)? Put your answer in fully reduced form.

Answer 1

the equation in slope intercept form would be
y=mx+b
y= 4/3x+6

Answer 2

Answer:

An equation of the line that passes through the points (-6, -2) and  (-3,2) will be:

• $y=\frac{4}{3}x+6$

Step-by-step explanation:

• Given the points (-6, -2) and  (-3,2)

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

$\left(x_1,\:y_1\right)=\left(-6,\:-2\right),\:\left(x_2,\:y_2\right)=\left(-3,\:2\right)$

$m=\frac{2-\left(-2\right)}{-3-\left(-6\right)}$

$m=\frac{4}{3}$

As we know that the point-slope form

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

substituting the values $m=\frac{4}{3}$ and the point (-6, -2)

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

$y-\left(-2\right)=\frac{4}{3}\:\left(x-\left(-6\right)\right)$

$y+2=\frac{4}{3}\left(x-\left(-6\right)\right)$

$y+2=\frac{4}{3}\left(x+6\right)$

Subtract 2 from both sides

$y+2-2=\frac{4}{3}\left(x+6\right)-2$

$y=\frac{4}{3}x+8-2$

$y=\frac{4}{3}x+6$

Therefore, an equation of the line that passes through the points (-6, -2) and  (-3,2) will be:

• $y=\frac{4}{3}x+6$