Question

Which is the equation of the line that passes through the points (-4, 3) and (2,-6)

Answer 1

first we have to find the slope by dividing the difference of the ys over the xs

-6 - 3 = -9 (y)
2 - -4 = 6 (x)

the slope is -9/6 or -3/2

now we plug the slop along with a set of points into the slope intercept formula (y=mx+b) to find b (the y intercept)

-6 = 2(-3/2) + b
-6 = -3 + b
-3 = b

so the equation would be y = (-3/2)x - 3

Answer 2

We want to find the equation of a line given that we know two points on the line.

The line is:

$y = \frac{-3}{2}*x - 3$

Let's see how to find the line equation.

We know that a line equation is written as:

$y = a*x + b$

Where a is the slope and b is the y-intercept.

If the line passes through the points (x₁, y₁) and (x₂, y₂), then the slope of the line is given by:

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

Here we know that the line passes through the points (-4, 3) and (2, -6), then the slope of our line is:

$a = \frac{-6 - 3}{2 - (-4)} = \frac{-9}{6} = \frac{-3}{2}$

Then the line is something like:

$y = \frac{-3}{2}*x + b$

To find the value of b, we can use one of the two points on the line.

For example, I will use the second one, (2, -6).

This means that when x = 2, y must be equal to -6.

Then we can replace that in the line equation and solve it for b:

$-6 = \frac{-3}{2}*2 + b\\\\-6 = -3 + b\\-6 + 3 = -3 = b$

Then the equation of the line is:

$y = \frac{-3}{2}*x - 3$

A graph of this line can be seen below, where the two points are also graphed.

If you want to learn more, you can read:

https://brainly.com/question/21637716