Coordinate Geometry Formulas to Help You Improve Your ACT Math Score
If you know how to use the right formulas, you can pick up a lot of extra points on the ACT Math section by simply filling in the right numbers and calculating the results. (We call this a plug-and-chug question.) Here are some coordinate geometry formulas for slope questions. Check your understanding on these samples and move on to a practice test when you feel ready.
The first thing you need to do with any formula is identify what each variable (or letter) stands for. The name of the formula will often help! In this case, you know the following has something to do with the slope and intercepts (where a line crosses the x-axis and y-axis).
y = mx + b
- x and y: Represent the coordinates of any given point on the line.
- Slope (m): Measures the steepness or incline of a line. You can use slope to find another point on the line.
- y-intercept (b): Is where a line intersects the y-axis.
- x-intercept: Isn't explicitly represented by a variable, but you would use this formula to find the x-intercept on the ACT! To do so, set y equal to zero and solve for x.
When the ACT asks you to solve for the slope, y-intercept, or x-intercept, write out this formula. Note that you'll often be given an equation in a different form. In this case, begin by rearranging it into the familiar form above and then solve. Take a look at the example below.
What is the slope of the line 5x – 11y = 7 in the standard (x, y) coordinate plane?A. –5
The question gives you an equation and asks you to find the slope, which tells you it's time to put the slope-intercept formula to use. Start by rearranging your line equation into slope-intercept form, y = mx + b, and paying close attention to any sign changes. The provided line is 5x – 11y = 7, so you'll want to move everything except y to the right of the equal sign.
Step 1: 5x – 11y = 7
Step 2: –11y = –5x + 7
Step 3: y = 5/11x – 7/11
Step 4: The slope, m, is 5/11.
The correct answer is (C).
Always choose the formula that matches the data you're given by the question. While the slope-intercept equation works great when you're given the intercepts, if you are only given two coordinates on a line, you'll need to use the slope formula.
As long as you don't mix up your x's and y's and pay attention to the signs, you can quickly solve this problem by plugging the coordinates into the slope formula. Note that sometimes your teacher may refer to slope as "rise over run" or rise/run.
What is the slope of the line that contains the points (6, 4) and (13, 5)?
Plug your points into the slope equation: (y2-y1) / (x2-x1).
The populated equation is as follows: (5-4) / (13-6).
The answer is 1/7, or (C). If you got (B), you may have mixed up your x and y pairings!
Once you master these two equations, you'll be able to work through these problems quickly and earn yourself a few more points on your ACT Math score. For more help preparing for the ACT, check out our book, ACT Premium Prep and subscribe to our YouTube channel for additional tips for testing success.