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!

 

Author

  • Kristin Fracchia

    Dr. Kristin Fracchia has over fifteen years of expertise in college and graduate school admissions and with a variety of standardized tests, including the ACT, SAT, GRE, GMAT, and LSAT, with several 99% scores. She had a PhD from the University of California, Irvine, an MA degree from The Catholic University, and BA degrees in Secondary Education and English Literature from the University of Maryland, College Park. She was the recipient of the 2013 Excellence in Teaching Award and the Chancellor’s Club Fellowship from the University of California, Irvine. She’s worked as a high school teacher and university professor, as an independent college and graduate school admissions counselor, and as an expert tutor for standardized tests, helping hundreds of students gain acceptance into premier national and international institutions. She now develops accessible and effective edtech products for Magoosh. Her free online content and YouTube videos providing test prep and college admissions advice have received over 6 million views in over 125 countries. Kristin is an advocate for improving access to education: you can check out her TEDx talk on the topic. Follow Kristin on LinkedIn!

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

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