Using Slope to Find a Missing Coordinate

Usually, we use the slope formula to find the slope of a line when we know two points on the line. But if we already know the slope of a line, we can use the slope formula to find a missing coordinate of a point on the line.

Here's the slope formula we'll be using:

Example

Find x if the line through the points (6, x) and (1, -5) has a slope of 2. Since the slope of the line is 2, we'll replace the m in our slope equation with 2. The two points will give us the numbers and variable that will replace the subscripted variables in the slope equation.

Be careful here! Did you notice that the x in the first point is really the y-coordinate of that point? Now we'll use the slope formula to find the value of x, the missing y-coordinate.

-10 = -5 - x

-5 = -x

-1(-5) = -1(-x)

5 = x

x = 5

OK, the answer is x = 5, but what does the answer mean? It means that if we substitute 5 for the missing coordinate in the first point, the slope of the line between the two points will be equal to 2. If you want to check this answer, just use the slope formula to find the slope of the line between (6,5) and (1,-5). If the slope of this line is 2, you know that your answer of x=5 is correct.