What is the Point Slope Formula?
The point slope formula is the equation of a straight line in the form:
y – y1 = m(x – x1)
In the point slope formula, y is the unknown y coordinate. y1 is the given y coordinate, which is to be placed in the formula.
Similarly, x is the unknown x coordinate. x1 is the given x coordinate, which is to be used in the formula.
Variable m represents the slope of the straight line.
Setting Up the Point Slope Formula
You can set up the point slope formula if you have the coordinates of one point on the line and the slope of the line.
We have already looked at slope in our post entitled What is Slope?
If you know this formula, go to the Free Geometry Review Problems
Now consider the following example:
You have a straight line with a slope of 1/2 and which passes through the point (6,2). Set up the point slope formula and the equation of the straight line.
First, we need to set up the point slope formula.
To set up the point slope formula, we need to put the information into the formula provided above.
y – y1 = m(x – x1)
y – 2 = 1/2(x – 6)
Then start to find the equation of the straight line by multiplying each side of the equation by 2 to get rid of the fraction.
y – 2 = 1/2(x – 6)
2 × (y – 2) = 2 × [1/2(x – 6)]
2y – 4 = x – 6
Then get the x variable to the other side of the equation.
2y – 4 = x – 6
2y – 4 – x = x – x – 6
2y – 4 – x = – 6
The next step is to deal with the integers.
2y – 4 – x = – 6
2y – 4 – x + 6 = – 6 + 6
2y – 4 – x + 6 = 0
Then rearrange the terms to get the formula for a straight line. The formula for a straight line is in this form: ax ± by ± c = 0
2y – 4 – x + 6 = 0
2y – x + 6 – 4 = 0
2y – x + 2 = 0
–x + 2y + 2 = 0
If you need to refresh your memory on the formula for a straight line, please see our post on solving linear equations.
Exam Questions on Point Slope Formula
You might see two different types of problems on the point slope formula on the exam.
Instructions for test problems might be worded like the following examples:
Set up the equation in point slope form.
Find the equation of a straight line.
You can also visit Purple Math for more information on the Point Slope form.