Eighth Grade · Math · week 4

Slope from graphs and tables

Compute slope as the constant rate of change (rise over run) from a table of values or a graph.

Slope measures how steep a line is -- how much y changes for every one step of x. Between any two points, slope = (change in y)/(change in x), often called "rise over run." A line climbing left to right has positive slope, a line falling has negative slope, and a flat line has slope zero.

From a table, pick any two rows and divide the change in y by the change in x. If the relationship is really a straight line, EVERY pair of rows will give the same slope -- checking a second pair is a built-in way to confirm you have a line at all.

📋 For the teacher
Teach it (10–15 min):
  • Trace "rise" (vertical) and then "run" (horizontal) physically with a finger on a graph -- up is positive, down is negative.
  • From a table: pick ANY two rows and divide the change in y by the change in x; getting the same number from a second pair of rows is the best proof the data is really linear.
  • Connect the sign of slope to a story they know: positive is climbing (savings growing), negative is falling (a candle burning down), zero is flat (no change at all).
  • Tie slope to a rate they already understand, like dollars-per-hour or miles-per-gallon, so it never feels like a bare graph trick.
Talk about it:
  • Why should slope come out the same no matter which two rows of the table you pick?
  • What would it mean if two different pairs of rows gave two different slopes?
  • How can you tell from a table alone whether a relationship is a straight line?

Mastery looks like: From either a table or two points, they compute slope as rise over run and confirm it with a second pair.

Common stumbles: Flipping rise and run (computing run/rise instead); losing track of which point is "first" and getting the sign backwards.

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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