ACT Math Tips: The One Equation of a Line You Need to Know

In Geometry class, there are several forms of an equation of a line that most students learn.

You learn standard form, slope-intercept form, point-slope form, etc., but for basically every single question that the ACT Math section asks you about lines on a coordinate plane, there’s only ONE you really need to know. Only ONE that is really useful.

The winner is…slope-intercept form, or y = mx + b.

Ding! Ding! Ding!

Slope-intercept form is so useful because, in order to answer many questions on the ACT, you will need to find: either the slope or the y-intercept, or you will be given the slope and a point and need to find the y-intercept, or something along those lines.

If you put an equation in slope-intercept form,y = mx + b, you will see this information instantaneously. In the equation y = mx + b:

  • m is the slope.
  • b is the y-intercept

So if an equation of a line is in this form, you don’t need to do any extra work to determine what these values are.

The ACT knows how powerful slope-intercept form is, so it will rarely give you an equation in this form. Instead, it will typically give lines in standard form, ax + by = c. So what you want to do, in most cases, is use your algebra skills to move this equation around to slope-intercept form.

Let’s say you have this equation of a line: 2x + 4y = 12. Move it around so that you have the y isolated on one side:

  • 2x + 4y = 12
  • 4y = - 2x + 12
  • y = (- 2x + 12)/4
  • y = -2/4 x + 12/4
  • y = -1/2 x + 3

Now we can see that the slope of this line is -1/2and the y-intercept is 3, and that’s very valuable information.

Check out the video above for examples on how this works in real ACT-like problems!


By the way, Magoosh can help you study for both the SAT and ACT exams. Click here to learn more!

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