Finding Slope from an Equation
There are a few different ways to find the slope of a line: from its depiction on a graph, from a set of points, and from an equation. In this lesson, we’re going to take a look at the last of these. Specifically, we’re going to look at slope-intercept form, and how it will appear on the GED Math test.
Slope-intercept form is just a fancy name for the type of equation that describes a straight line. This equation is on the GED formula sheet, so you don’t need to memorize it! It is written like this: y = mx + b, where m is the slope and b is the y-intercept. The y-intercept is where the line crosses the y-axis (the vertical one). The x and y values represent coordinates along the line.
Consider this equation in slope-intercept form: y = 4x + 3. Just by glancing at it, we can tell that it describes a line with a slope of 4 and a y-intercept of 3. In other words, the line goes up 4 units for every unit it moves to the right, and it crosses the y-axis at 3. If we want to find the coordinates of various points along the line, all we have to do is substitute in values for x or y and then solve for the other coordinate. In the example equation, an x-value of 2 would mean that y = 11, so the line must pass through (2,11).
On the GED Math test, however, you are more likely to be asked to use such an equation to find slope. Sometimes, the equation will already be in slope-intercept form. If it’s not, just rearrange the equation to solve for y.
Let’s look at another example, the equation 2x + 3y = 6. To begin with, we subtract 2x from each side, leaving us with 3y = -2x + 6. (We put the -2x in front of the 6 because we are aiming for slope-intercept form.) Then, we divide each side by 3, which gives us y = -2/3 + 2. The equation is in slope-intercept form; the line has a slope of -2/3 and passes through the y-intercept at 2. Occasionally, you will end up with an equation in slope-intercept form that doesn't have a value for b, like y = 4x. This means that the y-intercept is 0. It’s just that simple. Here are some practice exercises for you to work on!