Lesson · Grade 10 · Foundations of Mathematics and Pre Calculus
Slope: rise over run
- Grade 10
- Foundations of Mathematics and Pre Calculus
- 1 min 58 s
- British Columbia
- BC10-MA-12
A step triangle drawn on the line through (1, 2) and (4, 11) gives a run of 3 and a rise of 9, so the slope is 9 ÷ 3 = 3. Stepping 1 across and 3 up checks this, and the formula (y₂ − y₁) ÷ (x₂ − x₁) gives 3 again. The video then shows two common mistakes and a ramp with a slope of 1/12.
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In one sentence
The question this lesson answers
How steep is this line? We measure steepness with a number called the slope.
The line passes through the point 1, 2 and the point 4, 11.
Transcript
What the lesson says
How steep is this line? We measure steepness with a number called the slope.
The line passes through the point 1, 2 and the point 4, 11.
The slope is the rise divided by the run. A step triangle on the line shows both.
The run is the change in x, how far we move across: 4 minus 1, which is 3.
The rise is the change in y, how far we move up: 11 minus 2, which is 9.
So the slope is 9 divided by 3, which is 3.
Check it: for every 1 across, the line goes up 3. Step by step, that makes 3, then 6, then 9.
For a formula, call the first point x one, y one, and the second x two, y two.
The slope is y two minus y one, divided by x two minus x one.
Here that is 11 minus 2 over 4 minus 1, which is 9 over 3, or 3. The same answer.
A common mistake is putting the run on top. 3 over 9 is one third, which is not the slope.
Another mistake is subtracting in different orders. 11 minus 2 over 1 minus 4 is 9 over negative 3, or negative 3, which is wrong.
Keep the same order on top and bottom. 2 minus 11 over 1 minus 4 is negative 9 over negative 3, which is 3.
A ramp that rises 1 metre over a run of 12 metres has a slope of 1 over 12.
Slope is rise over run: the change in y divided by the change in x.
Curriculum
Where this fits
- British Columbia, Grade 10
Foundations of Mathematics and Pre Calculus 10, Linear relations: linear functions: slope and equations of linesBC10-MA-12
Next: Four Kinds of Slope: Uphill, Downhill, Flat and a Wall
The outcomes and strands follow the British Columbia curriculum.
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