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

Recall that the slope, m, of a line between two points, (x_{1}, y_{1}) and (x_{2}, y_{2}), is given by the following formula:

m = rise/run = (y_{2} - y_{1})/(x_{2} - x_{1})

You are given the following:

slope: m = -1/3

point 1: (x_{1}, y_{1}) = (7, -9)

point 2: (x_{2}, y_{2}) = (x, -13)

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

m = (y_{2} - y_{1})/(x_{2} - x_{1})

-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