I’m so excited to talk about the #1 method for finding a slope without using a formula! Through my years of teaching, I have found that my students struggled with the slope formula. So instead of using just the formula, I disguised the formula in a slightly different way that students would understand! We can use this #1 method to find slope without a formula and apply it to finding slope from a graph, two points, from an equation, and so on! If you need to find a slope, this method is for you!
Finding Slope
Let’s talk about finding a slope and what a slope is! First, we need a line! The slope is the steepness of a line as it moves from LEFT to RIGHT. The slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line. The slope of a line is always constant (it never changes) no matter what 2 points on the line you choose.
When would slope be important in the real world? Have you ever seen a spiral staircase in a house? The reason may be for design features, but in reality, a staircase most likely wouldn’t fit because the slope would be too steep to climb up the stairs!
Want to skip reading and watch instead? Don’t worry I got you covered!
Formula for Finding Slope
The formula or the equation for finding slope is m=y2-y1/x2-x1
Where m = slope and (x1, y1) and (x2, y2) are points found on the line.
Finding Slope with Two Points
So how are we going to disguise this formula to make it easier to remember how to find the slope? We are going to put the formula into a table like this ⬇️
Next, we will find the change in the y values by using a vertical number line. I like to just use the words “what is the change in y values and does the number go up or does the number go down”?
Then repeat this for the change in x values.
Then you simply write your change in y over your change in x. Simplify if necessary and then voila you now have your slope!
How to Find Slope from a Graph
You can either pick 2 points from the line and use the table method or you can count how many units you rise over how many units you run. You can “rise” up or down, but I always like to go up because rise means up! Then you can “run” right if you are moving towards the positive numbers or you can “run” left if you are moving towards the negative numbers.
You can always check with Slope Dude if you need to remember whether your slope is positive or negative.
Finding Slope of an Equation
If you want to find the slope of an equation, the equation needs to be in Slope-Intercept Form. Slope-Intercept Form: y = mx + b
M = slope
B = y-intercept.
If your equation is in Standard Form Ax + By = C, your slope = -A/B or you can solve for y. Then all you do is identify your slope in the equation y = mx + b and that is it!
Do you need any more slope practice? Check out these slope resources!
Love, Robin
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