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Teaching video
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Grade 9 chapters and video availability01 · Read and understand
What you will learn
- Use point-slope form and translate it into slope-intercept form.
- Justify the method and check its domain, units, or logical conditions.
Before you start
Signed arithmetic, fraction and decimal operations, one-step equations, and introductory coordinate graphs.
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
Find the line of slope 3 passing through (2,7).
Why this math matters
Construct a linear model from one observed point and an independently known constant rate. The example connects a stated condition to a conclusion and then checks whether the result satisfies that condition.
Set up the model
A useful answer starts with clear assumptions:
- Use the real-number system and the restrictions or data model stated in the question unless another domain is specified.
- Treat provided measurements as exact classroom-model values unless an approximation or uncertainty is stated.
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.
Build a line from a point and a rate
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Find the line of slope 3 passing through (2,7).
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 conditions
y−7=3(x−2)
The change from the known point has vertical-to-horizontal ratio three.
Develop the calculation
y−7=3x−6
Distribute the slope across the horizontal difference.
Check and interpret
y=3x+1
At x=2 the rule returns seven, and its constant rate is three.
The result
y=3x+1
At x=2 the rule returns seven, and its constant rate is three.
Common mistakes to catch
- The known point need not lie on an axis.
- Distribute a negative slope to both terms inside parentheses.
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
Write a line of slope −2 through (1,4).
Show a hint
Use y−4=−2(x−1).
Reveal answer and explanation
y=−2x+6
Expanding and adding four gives the stated intercept.
Practice 2
Does the given point's y-coordinate always equal the y-intercept?
Show a hint
An intercept has x=0.
Reveal answer and explanation
No
The point (2,7) is on the main line, but its y-intercept is (0,1).
Take the idea with you
Construct a linear model from one observed point and an independently known constant rate.
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: Distinguish zero slope from undefined slope
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