Passes through the points (-2 , -9) and (-4 , -6)

Answer 1

Good afternoon and thank you for the question!

The answer is y = -(3/2)x - 12 is line passing through both points.

Below is an explanation of how I arrived at the answer:

We need two points to define a line. In this case, we have the (x,y) pairs: (-2,-9) and (-4,-6).

Now, we can use the following equation and the two (x,y) pairs above to get the slope of the line:

y₂-y₁ = m(x₂-x₁), hence,

-9+6 = m(-2+4), so -3 = 2m and m = -(3/2).

Now that we have the slope, we use the following equation and one of the (x,y) pairs to get the equation for the line (note, it does not matter which (x,y) pair we choose, we still get the same answer). Using (-2,-9), and y-y₁ = m(x-x₁), we have:

y + 9 = -(3/2)(x+2) = -(3/2)x - 3, so

y = -(3/2)x - 12