Find x if the slope between (7,-9) and (x,-13) is -1/3

Question

Find x if the slope between (7,-9) and (x,-13) is -1/3

Answer 1

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

-1/3 = (-13 - -9) / (x – 7)

Solving that algebraically for the value of “x” yields

-1/3 = -4 / (x – 7)

-1/3 * (x – 7) = -4

x – 7 = -4(-3)

x – 7 = 12

x = 19

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 :)

Answer 2

Recall that the slope, m, of a line between two points, (x₁, y₁) and (x₂, y₂), is given by the following formula:

          m = rise/run = (y₂ - y₁)/(x₂ - x₁) 

You are given the following:

          slope:   m = -1/3

          point 1:   (x₁, y₁) = (7, -9)

          point 2:   (x₂, y₂) = (x, -13)

You are asked to solve for x, which is represented by x₂ in point 2. To do so, plug in all the given info into the slope formula and solve for the missing variable:

          m = (y₂ - y₁)/(x₂ - x₁) 

       -1/3 = (-13 - (-9))/(x - 7)

       -1/3 = (-4)/(x - 7)

      Cross multiply to get rid of the fractional expressions 

   -1(x - 7) = 3(-4)      

      Multiply each term inside parenthesis on left-hand side of equation by -1 

      -x + 7 = -12          

      Subtract 7 from both sides of the equation 

            -x = -19       

      Divide both sides of the equation by -1 to solve for x 

             x = 19 

Answer 3

Find x if the slope between (7,-9) and (x,-13) is -1/3

slope between two points:

slope = (y2 - y1)/(x2 - x1)

plug the given data from the problem and solve for x:

-1/3 = (-13 - (-9))/(x - 7)

-1/3 = (-13 + 9)/(x - 7)

-1/3 = (-4)/(x - 7)

cross -multiplying:

3(-4) = -1(x-7)

-12 = -x+7

-19 = -x

19 = x