Find the equation of the line through (4,2) and (-2,3).

Question

just want to check if my answer is correct i got y=-1/2x

Answer 1

if I substitute x=4 into your equation, then y comes out as-2, which is not correct.

let's calculate slope m: m = (3-2)/(-2-2) = -¼.

now use point slope form and come up with the correct equation (make sure that (-2,3) satisfies it).

Answer 2

Slope formula is (y₂ - y₁) / (x₂ - x₁)

(3 - 2) / (-2 - 4) = 1 / -6, or -¹/₆

 

Now that we know the slope, we can use the point-slope formula:

y - y₁ = m(x - x₁)

y - 2 = -¹/₆(x - 4)

y - 2 = -¹/₆ x + ²/₃

y = -¹/₆ x + 2 ²/₃

 

Check by putting in one of the points given:

3 = -¹/6 * -2 + 2 ²/₃

3 = ¹/₃ + 2 ²/₃

3 = 3