What is an equation of the line that passes through the points (4,8) and (-2,-7)

Answer 1

Method 1:

Find the slope (m) using the slope formula:

where (x₁, y₁) = (4, 8) or x₁ = 4, y₁ = 8

and (x₂, y₂) = (-2, -7) or x₂ = -2 and y₂ = -7:

m = (-7 - 8)/(-2 - 4) = -15/-6 = 5/2

Then use the point-slope form of a line:

y - y₁ = m(x - x₁) and plug in x₁ = 4, y₁ = 8, and m = 5/2:

y - 8 = (5/2)(x - 4)

There are a lot of other methods to use as well.

Answer 2

Since two points are given start with two-point form

(y - 8) / (x - 4) = (-7 - 8) / (-2 - 4)

Simplify and answer.

Answer 3

Hello Drake,

For your question.

Recall that the equation for a line in point-slope form is:

(y - y0) = m*(x - x0) where (x0,y0) is either (4,8) or (-2,-7), the choice is yours and our slope 'm' = (y0 - y1)/(x0 - x1) where (x1,y1) would either be (4,8) or (-2,-7) depending on your choice of (x0,y0). Just remember to keep your choices consistent once you pick them, meaning if you pick (x0,y0) = (4,8), then (x1,y1) = (-2,-7) and vice versa.

To keep things concrete, let's say (x0,y0) = (4,8) and (x1,y1) = (-2,-7).

Then for our slope 'm' = ((8)-(-7))/((4)-(-2)) = (8+7)/(4+2) = 15/6 = 5/2

Now let's assemble our line since we have all the necessary components.

Now,

(y - y0) = m*(x-x0)

(y - (8)) = (5/2)*(x - (4))

You are welcome to simplify it further if you are instructed to do so. I will leave that to you.

Hope this helps!