rate of change and slope

Question

(-12,9) (x,-2) slope: -1/2

Answer 1

Hi Haley to solve this problem all you need is the slope formula:

slope=( y₂ - y₁)/ (x₂-x₁)

so you just need two points in that case are already given the slope so you just have to fill in the formula with the given information and find the missing variable. So let’s say the first point is (-12,9) this means that x₁= -12 and y₁= 9. The second point is (x,-2) so x₂ is the missing variable that we want to find and y₂= -2. It’s now time to plug in the formula:

-1/2 = (-2-9) / (x₂+12)

note: x₂-(-12)= x₂+12

-1/2 = (-11)/ (x₂+12) from the first step to the second we did -9-2 which gives us -11 because they have the same sign we add the numbers and put the sign of the numbers which is (-)

Finally we’re going to do cross multiplying:

ex: A/B = C/D gives us A.D= B.C we’re going to apply the same strategy here

(-1) (x₂+12) = 2 (-11)

(-1) (x₂+12) = -22

now distribute (-1) to (x₂+12):

-x₂-12 = -22

now add +12 to both sides so that we can get rid of the -12 on the right side and isolate x₂:

-x₂ -12 +12 = -22 +12

-x₂ = -10 multiply both sides by (-1) to get x₂:

x₂ = 10

Answer 2

These are tricky! How do we find slope?

(y₂ - y₁)/(x₂ -x₁)

Here's the trick: Either point can be (x₁,y₁) or (x₂,y₂).

(-2 - 9)/(x - (-12)) = -1/2

(-1/2)(x + 12) = -11

(-1/2)x - 6 = -11

(-1/2)x = -5

x = 10

Let's check, this time going the other direction.

(9 - (-2))/(-12 - 10) = 11/-22 = -1/2

Boom.