Given the points (-3,9) and (6,-6), write the equation of the line.

Answer 1

You can use the POINT-SLOPE formula y -y₁ = m(x - x₁) but you need to calculate the slope, m.

Use the points given to calculate the slope, m = (y₂ - y₁)/(x₂ - x₁)

Doesn't matter which point you make (x₁, y₁) and (x₂, y₂), the slope will be the same.

I picked P₁ = (-3, 9) and P₂ = (6, -6)

So slope, m = (-6 - 9)/(6 - (-3)) = -15/9 = -5/3

If you were to plot the points and connect them, you will see that the line slants downward showing that the slope is negative.

Pick one of the given points and plug the x, y and the calculated m into the POINT-SLOPE formula

y - (-3) = -5/3(x - 9)

y + 3 = -(5/3)x + 15 ....This is where 15 comes from: (-5/3 times -9) = factor to get POSITIVE 15

y = -(5/3)x + 15 - 3 ... bring the 3 over from the LHS to isolate the y term

y = -(5/3)x + 12 Final Answer

Answer 2

Use two-point form

(y - 9) / (x + 3) = (-6 - 9) / (6 + 3)

Answer 3

1) Find your slope using m = (y2-y1) / (x2-x1)

m = (-6 - 9) / (6 - (-3))

= -15 / 9 = -5/3

2) Find your intercept

-6 = -15/9 * 6 + b

-6 = -90/54 + b

-6 = -5/3 + b

-6* (-3/5) = b

b = 18/30 = 3/5

3) Write your equation

y= -5/3 x + 3/5