Question

What is the equation for the line that passes through (-4,-3) and (-2,3)

Answer 1

Answer: $y=3x+9$

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

We can calculate the slope of the line with this formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Given these points:

$(-4,-3)\\\\ (-2,3)$

We can identify that:

$y_2=-3\\y_1=3\\\\x_2=-4\\x_1=-2$

Then, the slope is:

$m=\frac{-3-3}{-4-(-2)}=3$

Now we have to substitute the slope and one of the points into $y=mx+b$ and solve for "b":

$3=3(-2)+b\\\\3+6=b\\\\b=9$

Then, the equation of this line is:

$y=3x+9$