Slopes
Compare slopes using rise, run and relationships between lines. Then move the points to explore how the slopes change.
Signed rise and run
1 comparison · No time limit · Explore after checking
Example
Example
Compare the slope of line PQ with Quantity B.
Review the comparison
From P to Q, the horizontal change is +5.
The vertical change is +3. Both axes use the same unit.
Equal axis scales. The two changes stay fixed if the line moves up or down.
Slope of PQ
2/5
Choose an answer to try the example.
Why?
Explore the relationship
Place P and Q equally far above and below the x-axis.
In this drawing
Need a clue?
Their heights must be opposites, so their average must be zero. Keep the signed rise fixed.
Example positions
Move the line vertically. Its height changes, but its signed rise and run stay the same.
The controls preserve the givens. Examples illustrate the rule; the explanation proves it.
Go further Apply the idea
Further practice does not change your comparison score.
Continue your unfinished round
Your answers are saved in this tab. Continue from where you left off.
Continuing uses no additional practice start.
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Your answers from this round will be discarded. You can choose your settings before starting a new round.
Starting the new round uses one practice start.
- Answered
- 0 / 1
- Active time
- 0:00
Round complete.
Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is usedHelp
Choose whether Quantity A is greater, Quantity B is greater, the quantities are equal, or the relationship cannot be determined. Use only the stated givens. A drawing shows one possible case.
Your first checked answer counts. A shown answer counts as 0 correct. A checked comparison is saved immediately, so you can explore afterward without losing your result. An unfinished comparison is not saved as a result.
After checking, use the controls to solve an exploration goal. When the relationship cannot be determined, save two valid cases with different comparisons. Open Go further to apply the idea to a new question. These activities are optional and do not change your score.
Angles and trigonometric functions use degrees. Levels increase the mathematical complexity; they do not measure IQ.
About this practice
Learn a method
Read rise over runCompare slopes using rise, run and relationships between lines. Then move the points to explore how the slopes change.
For a broader mix of practices, explore the geometry practice test. Membership is required to start a test.
Report a problem
Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is used