slope between

Question

Find x if the slope between (2,1) and (x,9) is 2

Answer 1

Recall the slope (m) when given two points, (x₁, y₁) and (x₂, y₂), is defined by the following formula:

     Slope =  m =  (y₂ - y₁) / (x₂ - x₁ ) 

You are given the following:

     m = 2

     (x₁, y₁) = (2, 1)

     (x₂, y₂) = (x, 9)

This means you are looking to solve for x₂ in the slope formula. To do so, plug in the given values for slope and the two points into the formula:

     2 =  (9 - 1) / (x₂ - 2)

     2 =  (8) / (x₂ - 2)

After we cross multiply, we get the following:

     2·(x₂ - 2) = 8

Now we divide both sides of this equation by 2:

     (2·(x₂ - 2))/2 = 8/2

     x₂ - 2 = 4

Adding 2 to both sides of the equation, we solve for x₂ :

     x₂ - 2 + 2 = 4 + 2

     x₂ = 6

Thus, for the point (x, 9),  x = 6.

Answer 2

Hello, thank you for taking the time to post your question!

The underlying slope equation that you want to use here is m=(y2​−y1​)/(x2​−x1​) … for this set of values that means

2=(9−1) / (x−2)

Solving that algebraically for the value of “x” yields

2=8/(x−2)

2∗(x−2)=8

x−2=8/2

x−2=4

x=6

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)