Write the equation of the line that passes through the points (-8,-6) (and (-4,2). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line

Answer 1

We will be using the slope formula to calculate m, or the slope of the line that passes through the points (-8, -6) and (-4, 2).

Remember, when you are calculating the slope from two given points, you are finding the change in y over the change in x.

P_{1 = (} x_1, y_{1 )}

P_{2 = (} x_2, y_{2 )}

m = Δy / Δx _---> m = (y₂ - y₁) / (x₂ - x₁)

Now let's assign the given points:

(-8, -6) --> x₁ = - 8 & y₁ = -6

(-4, 2) --> x₂ = -4 & y₂ = 2

Now, let's plug these values into the slope formula:

m = (y₂ - y₁) / (x₂ - x₁)

= (2 - (-6)) / ((-4) - (-8))

Let's simplify:

(2 - (-6)) / ((-4) - (-8))

= (8) / (4)

= 2

Therefore, the slope, or m, is 2.

Now that we have found the slope, let's write out the final equation in point-slope form.

What is required for the equation is a slope, and any pair of points on the line. Since we were given two to choose from, I will use (-4, 2) in this case.

Remember, the point-slope formula is: y - y₁ = m (x - x₁)

In terms of this formula:

m = 2

y₁ = 2

x₁ = -4

Let's plug in these values into the point slope formula and simplify:

y - y₁ = m (x - x₁)

y - (2) = (2)(x - (-4))

y - 2 = 2(x + 4)

y - 2 = 2x + 8

y = 2x + 10

Therefore, our final answer is: y = 2x + 10