Slope – Practice Problems

Having fun while studying, practice your skills by solving these exercises!

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Slope measures the incline of a line. You can also think of this as the number that represents the steepness of a line. To calculate the slope, you can use the slope formula which is the change in the height compared to the change in the width. Using ordered pairs, this is the change in the y-values divided by the change in the x-values or the rise divided by the run.

How can you use the value of slope to compare the steepness of lines? The greater the absolute value of the slope, the more steep the incline. Slopes can be positive or negative. Often students are told to remember this information using a mountain analogy (let’s hit the slopes!).

For a positive slope, the line goes up the mountain and for negative slopes, the lines go down the mountain. I am positive it is more difficult to walk up a mountain – do you get my drift? What if there is no incline? Then the slope is zero, and if the line is vertical, the slope is not defined. Does this seem like a lot to remember? Watch this video on slope, and you will learn some helpful tips to remember this very important information, so you won’t go bombing on the Bunny Slope.

Use slope to create equations of the line. CCSS.MATH.CONTENT.HSG.GPE.B.5

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Exercises in this Practice Problem
Label the picture using the correct terms.
Determine the slope of the mountainside.
Examine the slopes of the lines using the formula $m = \frac{\Delta y }{\Delta x}$.
Determine the slopes of the different routes.
Describe how the slope influences the look of a line in the coordinate plane.
Calculate the height of the mountain.