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Kristin Fracchia

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.

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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!


About Kristin Fracchia

Dr. Kristin Fracchia currently focuses on our MCAT and LSAT Prep, but she also has expertise in a wide range of standardized tests, including the ACT, SAT, GRE, and GMAT, as well as college and grad school admissions. With a PhD from UC Irvine and degrees in Education and English, she’s been working in education since 2004. She enjoys the agony and bliss of long distance trail running, backpacking, hot yoga, and esoteric knowledge.

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