Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Find the y-intercept from an equation, table or graph
Algebra
CCSS 8.F.B.4England: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Find the y-intercept from an equation, table or graph.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Graphs of linear equations y = mx + b
Leads to: Write y = mx + b from a slope and intercept, or from a graph; Write a linear function rule from a table; Find where a line crosses the x-axis
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Graphs of linear equations y = mx + b). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Does the point (1, 4) lie on the line y = x + 4? (Yes / No) → NoPrompt: Substitute the x-value into the equation.
- Does the point (0, −3) lie on the line y = 4x − 3? (Yes / No) → YesPrompt: Substitute the x-value into the equation.
- Does the point (−1, 8) lie on the line y = −4x + 5? (Yes / No) → NoPrompt: Substitute the x-value into the equation.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Find the y-intercept from an equation, table or graph. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: What is the y-intercept of y = 4x − 9?
- Step 1: x = 0 → y = −9
- Answer: -9
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- What is the y-intercept of y = 3 − 5x? → 3Prompt: The y-intercept is the value of y when x = 0.
- x: 1, 2, 3, 4. y: 2, 5, 8, 11. The pattern is linear. What is the y-intercept? → -1Prompt: Work out how much y changes when x goes up by 1.
You do: independent practice · 10 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- What is the y-intercept of y = 5x + 4? → 4Prompt: The y-intercept is the value of y when x = 0.
- x: 1, 2, 3, 4. y: −4, −9, −14, −19. The pattern is linear. What is the y-intercept? → 1Prompt: Work out how much y changes when x goes up by 1.
Watch out for
- Doing an operation to one side of an equation but not the other.
- Reading 3x as 3 + x, or thinking x always stands for one particular number.
Support and stretch
Support
- Review first: Graphs of linear equations y = mx + b.
- Use concrete materials: balance scales or a balance drawing.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Move on to: Write y = mx + b from a slope and intercept, or from a graph; Write a linear function rule from a table; Find where a line crosses the x-axis.
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-8.
Free lesson plan from eurekami.com/lesson-plan-builder