Learn with Amar
Teaching video
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Grade 9 chapters and video availability01 · Read and understand
What you will learn
- Find parallel and perpendicular line slopes with the appropriate exceptions.
- 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 lines through (0,1) parallel and perpendicular to y=2x−3.
Why this math matters
Use algebraic directions to verify a right-angle or parallel relationship in a coordinate drawing. 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 Euclidean geometry and the angle, parallelism, similarity, or congruence conditions stated; a sketch alone does not establish them.
- 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.
Use slope to compare nonvertical directions
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Find lines through (0,1) parallel and perpendicular to y=2x−3.
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
Given slope = 2
The intercept changes position, not direction.
Develop the calculation
Parallel slope = 2; perpendicular slope = −1/2
For nonvertical, nonhorizontal lines, perpendicular slopes have product negative one.
Check and interpret
Parallel: y=2x+1; perpendicular: y=−x/2+1
Both use the required point and their slopes supply the required direction.
The result
Parallel: y=2x+1; perpendicular: y=−x/2+1
Both use the required point and their slopes supply the required direction.
Common mistakes to catch
- Equal slopes also occur for the same line, so distinguish coincident from distinct parallel lines.
- Handle horizontal and vertical directions separately.
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
What slope is perpendicular to −3/4?
Show a hint
Take the negative reciprocal.
Reveal answer and explanation
4/3
(−3/4)(4/3)=−1.
Practice 2
What line through (2,5) is perpendicular to the horizontal line y=1?
Show a hint
A horizontal direction is perpendicular to a vertical one.
Reveal answer and explanation
x=2
The zero-slope case needs a vertical line, not a finite reciprocal slope.
Take the idea with you
Use algebraic directions to verify a right-angle or parallel relationship in a coordinate drawing.
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: Shade a half-plane from a linear inequality
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