4. If a line goes through the points (-3, 10) and (2, 5), write an equation.

Answer 1

Hi Aidan M.

With the points (-3,10) and (2, 5)

Let (-3,10) be your first point (x_1, y₁)

Let (2,5) be your second point (x_2, y₂)

For a line in Slope Intercept Form

y = mx + b

First use the two points given to find the slope

Second use one of the points to solve for b

Then just plug everything into your line

m = (y₂ - y₁)/(x₂ - x₁)

m = (5 - 10)/(2 -(-3)) = -5/5 = -1

Slope m = -1

y = -x + b

Now just solve for b

I will use your first point (-3, 10)

10 = -1(-3) + b

10 = 3 + b

10 - 3 = b

b = 7

y = -x + 7

You can graph this at Desmos.com. Of course there are other way to solve you can also try the Point Slope Form and see if you get y + x = 7 give it a try.

Answer 2

Hi Aidan!

Here's a video explanation of some steps for these types of problems. Hope it helps!

~Anika