Finding Slope from Two Points

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There are always a few questions about slope on the GED Math test. In math, slope is the steepness of a straight line on a graph. In one of the most common question formats, you are given the coordinates for two points and asked to find the slope of the line that passes through them.  

Coordinates are pairs of numbers that show the precise location of a point on a graph. They are written (x, y), because the first number indicates position on the x-axis (the horizontal one), and the second indicates position on the y-axis (the vertical one). A point at (2, 3), for example, is two places to the right of the 0 on the x-axis, and three places above the 0 on the y-axis.  

As for slope, the good news is that the formula you need is on the GED formula sheet. They have it written as m = (y2 − y1)/(x2 − x1), with m standing for slope for reasons that you don’t need to worry about. The little numbers, called subscripts, indicate the order in which the coordinates should be substituted. So if you are given two points like (2, 4) and (3, 5), the formula is (5 − 4)/(3 − 2) = 1/1 = 1. The line has a slope of 1.

In other places, you might see the slope formula as m = rise/run or m = Δyx (the Δ symbol means “the change in”). The important thing to remember is that slope is a rate; all of these formulas are saying “the line goes up (or down) by this many units for every unit it goes from left to right.”  

With that in mind, you can see how the value of the slope describes the line. If the slope is 1, it means that the line goes up by one unit every time it goes across one unit. If the slope is bigger than 1, the line goes up more than one unit every time it goes across one unit. If the slope is negative, the line slopes down from left to right.  

There are a couple of important special cases. When the slope ends up with a zero in the numerator (0/4, for example), the line is horizontal. In other words, it doesn’t rise or fall as it moves from left to right. If the slope has a zero in the denominator, it is vertical (doesn’t move from left to right at all). Dividing by zero is mathematically nonsensical, so vertical lines are often said to have an “undefined” slope.  

That’s all you need to know when it comes to finding slope from two points. Here’s a short quiz so you can practice what you’ve learned. Good luck!