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Teaching video
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Grade 8 chapters and video availability01 · Read and understand
What you will learn
- Explain how to explain constant slope with similar triangles.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Coordinate differences, ratios, and similar triangles.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
A straight line passes through (0,1), (2,5), and (5,11). Compare slopes from the first point to each of the other two and explain why they agree.
Why this math matters
Right triangles drawn along one straight line have equal rise-to-run ratios because their corresponding angles match. Choose convenient pairs of points on a straight graph; similar triangles ensure the slope stays the same.
Set up the model
A useful answer starts with clear assumptions:
- The listed points lie on one nonvertical straight line.
- Horizontal and vertical coordinate scales are fixed.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Explain constant slope with similar triangles
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A straight line passes through (0,1), (2,5), and (5,11). Compare slopes from the first point to each of the other two and explain why they agree.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the quantities
first rise/run = (5 − 1)/(2 − 0) = 4/2 = 2
Use one right triangle with horizontal run 2.
Apply the relationship
second rise/run = (11 − 1)/(5 − 0) = 10/5 = 2
The larger right triangle has the same rise-to-run ratio.
Check and interpret
Both slopes are 2
Each triangle has a right angle and the same angle along the line, so they are similar and their leg ratios agree.
The result
Both slopes are 2
Each triangle has a right angle and the same angle along the line, so they are similar and their leg ratios agree.
Common mistakes to catch
- Rise and run must use the same point order in their subtractions.
- A vertical line has zero run, so this quotient is undefined.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
A straight line has rise 12 for run 3. What rise corresponds to run 5 in the same direction?
Show a hint
Keep rise/run equal to 4.
Reveal answer and explanation
20
The slope is 12/3 = 4; rise = 4 × 5 = 20.
Practice 2
A line falls 6 units while x increases by 2. What is its slope?
Show a hint
A fall gives a negative vertical change.
Reveal answer and explanation
−3
Slope = −6/2 = −3.
Take the idea with you
Choose convenient pairs of points on a straight graph; similar triangles ensure the slope stays the same.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Recover a linear rule from a table
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