(Algebra > Relations & Functions > Functions)

One of the more difficult concepts for teachers to teach and for students to grasp is linear equations. To begin, students must understand slope. Since most students already understand “steepness” you can stress that slope is the measure of the steepness of a line. You can later discuss rate of change, after they get the basic meaning of slope.

Take some time to make sure students understand that the slope is the ratio of the vertical distance to the horizontal distance. Some students may find it easier to remember the ratio as “rise over run.”  As students complete subsequent pages, watch out for the common error of using the ratio in the wrong order. You may notice that this introductory document consists of problems with positive slopes only. Negative, zero, and undefined slopes, as well as finding slopes using coordinates are covered in other documents.  

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