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AL2025 8th Grade Math STAAR Test - Problem 1
How to match a rate to the correct graph by using slope
The student read 24 books in 15 weeks. That's a rate. Rate is the same thing as slope. So the slope you're looking for is 24 over 15, which simplifies to 8/5 or 1.6 books per week.
Now look at each graph and eliminate.
A is a horizontal line. A horizontal line has a slope of 0. That would mean the student read 0 books per week. That makes no sense. Eliminate it.
D is a vertical line. A vertical line has an undefined slope. It also doesn't represent a function. Eliminate it.
Now you're down to B and C. Both go up from left to right, so they both have positive slopes. The difference is how steep they are.
C has a low slope. The line rises slowly across the whole graph. If you read the points, it takes way more than 15 weeks to get to 24 books. That rate is too slow.
B has a steeper slope. The line passes through the origin and reaches 24 books right around 15 weeks. That matches the rate of 24 books in 15 weeks perfectly.
The answer is B.
When a question asks which graph models a rate, it's asking which graph has the right slope. Turn the rate into a fraction, then check which line actually rises at that speed. A line that's too flat has too small a slope. A line that's too steep has too large a slope. The right graph will hit the numbers they gave you at the right spot.
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