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 .
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,, you will see this information instantaneously. In the equation :
- 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: . Move it around so that you have the y isolated on one side:
Now we can see that the slope of this line is and 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!