8.EE.5: Unit Rate as Slope
Also written as 8.EE.B.5 and CCSS.MATH.CONTENT.8.EE.B.5 · Cluster: Understand the connections between proportional relationships, lines, and linear equations.
The Official Wording
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
Common Core State Standards, Grade 8, Expressions & Equations · Read it at the source · Checked October 14, 2026
What 8.EE.5 Means in Plain English
Eighth graders graph proportional relationships and read the unit rate as the slope: a printer making 90 pages in 3 minutes is a line through (0, 0) and (3, 90), rising 30 pages per minute. Then they compare it with a second printer, y = 25x.
Slope is the new word, and 8.EE.6 explains why it is the same anywhere on a line. Proportional lines become one kind of linear function (8.F.3), and in high school slope grows into average rate of change over an interval (HSF-IF.6).
8.EE.5 I Can Statements
- I can graph a proportional relationship from a table or equation.
- I can read the unit rate as the slope of the line.
- I can compare two rates shown as a graph and an equation.
8.EE.5 Worked Example
One pump given as a graph, the other as an equation, and the unit rate decides which is faster.
Pump A’s graph of gallons against minutes is a straight line through (0, 0) and (4, 30). Pump B pumps g = 8m gallons in m minutes. Which pump is faster?
- Pump A’s line passes through the origin, so the relationship is proportional. Read a clear point on it.(4, 30): 30 gallons in 4 minutes
- The unit rate is the rise for one minute of run, which is the slope of the line.slope = 30 ÷ 4 = 7.5 gallons per minute
- Pump B’s equation has the form y = kx, so its unit rate is the number multiplying m.Pump B: 8 gallons per minute
- Graph Pump B on the same axes through (0, 0) and (4, 32), and compare the two lines at 4 minutes.At 4 minutes: A at 30 gallons, B at 32
- The steeper line has the greater unit rate.8 > 7.5, so Pump B is faster
Check it: Fill a 600-gallon pool both ways: 600 ÷ 8 = 75 minutes for B and 600 ÷ 7.5 = 80 minutes for A, so B finishes first.
Common Mistakes with 8.EE.5
Reading slope as run over rise
(4, 30) gives a slope of 4/30
Try this: Say “output per one input” aloud: gallons per minute means gallons divided by minutes, 30 ÷ 4 = 7.5.
Judging steepness across different scales
“A looks steeper, so it is faster,” with one graph counting by 5s and the other by 2s
Try this: Compute each unit rate as a number before comparing; two graphs with different axis scales cannot be compared by eye.
Calling any straight line proportional
y = 8x + 5 called proportional with unit rate 8
Try this: Check that the line passes through (0, 0). y = 8x + 5 starts at 5, so y ÷ x is not constant.
Where 8.EE.5 Fits
Practice 8.EE.5
Quick Check
- A line through the origin passes through (5, 35). What are its unit rate and its equation?
- Car A travels d = 55t miles in t hours. Car B’s distance graph is a line through (0, 0) and (3, 171). Which is faster?
- On a graph of cost against pounds, a line through the origin rises $4 for every 2 pounds. What is the cost per pound?