🔮 Algebra Realm · Graphs
Rearranging to find gradient/intercept focuses on how to rewrite linear equations into y = mx + c form so their graph features become visible. In this lesson, focus on straight-line graphs connect coordinates, rates and equations.
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Rearranging to find gradient/intercept focuses on how to rewrite linear equations into y = mx + c form so their graph features become visible. In this lesson, focus on straight-line graphs connect coordinates, rates and equations.
Straight-line graphs connect coordinates, rates and equations. Gradient measures vertical change per horizontal step; the y-intercept records the value when x is zero. For rearranging to find gradient/intercept, the final written answer should make that exact relationship visible rather than hiding it inside an unexplained result.
Rearranging to find gradient/intercept: Straight-line graphs connect coordinates, rates and equations. Substitute one plotted coordinate into the equation or count a second rise-and-run triangle. Keep the rearranging to find gradient/intercept representation visible until the final line.
Plot draggable points on a coordinate plane, draw the line and compare its rise, run and axis crossing. Use the model to explain one change you notice while working on rearranging to find gradient/intercept.
Substitute one plotted coordinate into the equation or count a second rise-and-run triangle. Write that check beside the final rearranging to find gradient/intercept answer.
2y = 6x + 8 becomes y = 3x + 4.
Visual / interactive
Plot draggable points on a coordinate plane, draw the line and compare its rise, run and axis crossing. Use the model to explain one change you notice while working on rearranging to find gradient/intercept.
Worked examples
Understand the idea with small numbers, one representation and one clear step.
Use the standard Year 8 method with mixed examples and normal wording.
Handle multi-step or less familiar questions and explain choices.
Solve a worded question, show reasoning, check accuracy and write a final sentence.
Given information: Rearranging to find gradient/intercept — State the y-intercept of y = 3x + 2. Method choice: use the rearranging to find gradient/intercept method and show each step with the stated values. Calculation or reasoning: In y = mx + c, c is the y-intercept. Here c = 2. Final answer: 2. Check: substitute or compare with the original information to confirm the result fits the question.
Given information: Rearranging to find gradient/intercept — State the y-intercept of y = 3x + 14. Method choice: use the rearranging to find gradient/intercept method and show each step with the stated values. Calculation or reasoning: In y = mx + c, c is the y-intercept. Here c = 14. Final answer: 14. Check: substitute or compare with the original information to confirm the result fits the question.
Check: Read and, if useful, check m and c with a point.
Given information: Rearranging to find gradient/intercept — State the y-intercept of y = 3x + 13. Method choice: use the rearranging to find gradient/intercept method and show each step with the stated values. Calculation or reasoning: In y = mx + c, c is the y-intercept. Here c = 13. Final answer: 13. Check: substitute or compare with the original information to confirm the result fits the question.
Try explaining why each step works before checking the answer.
Given information: Rearranging to find gradient/intercept — State the y-intercept of y = 3x + 12. Method choice: use the rearranging to find gradient/intercept method and show each step with the stated values. Calculation or reasoning: In y = mx + c, c is the y-intercept. Here c = 12. Final answer: 12. Check: substitute or compare with the original information to confirm the result fits the question.
Substitute one plotted coordinate into the equation or count a second rise-and-run triangle. Write that check beside the final rearranging to find gradient/intercept answer.
Create a rearranging to find gradient/intercept problem with a tempting incorrect answer. Solve it, apply the check, and explain exactly where the incorrect method breaks down.
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Use plot patrol controls to solve three checked rearranging to find gradient/intercept rounds. Solve at least two of three marked rounds and use feedback to correct any error.
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Rearranging to find gradient/intercept: Straight-line graphs connect coordinates, rates and equations. Substitute one plotted coordinate into the equation or count a second rise-and-run triangle. Keep the rearranging to find gradient/intercept representation visible until the final line.
Tap to mark reviewedcoordinate · gradient · y-intercept · axis · linear relationship · rearranging · find
Tap to mark reviewedLabel and read both axes. Plot or identify ordered pairs as x first, then y. Use rise divided by run for gradient or read the y-axis crossing for intercept. Check the relationship with a second point or a table value. Record the check explicitly for rearranging to find gradient/intercept.
Tap to mark reviewed2y = 6x + 8 becomes y = 3x + 4.
Tap to mark reviewedGiven information: Rearranging to find gradient/intercept — State the y-intercept of y = 3x + 2. Method choice: use the rearranging to find gradient/intercept method and show each step with the stated values. Calculation or reasoning: In y = mx + c, c is the y-intercept. Here c = 2. Final answer: 2. Check: substitute or compare with the original information to confirm the result fits the question.
Tap to mark reviewedGiven information: Rearranging to find gradient/intercept — State the y-intercept of y = 3x + 14. Method choice: use the rearranging to find gradient/intercept method and show each step with the stated values. Calculation or reasoning: In y = mx + c, c is the y-intercept. Here c = 14. Final answer: 14. Check: substitute or compare with the original information to confirm the result fits the question.
Tap to mark reviewedGiven information: Rearranging to find gradient/intercept — State the y-intercept of y = 3x + 13. Method choice: use the rearranging to find gradient/intercept method and show each step with the stated values. Calculation or reasoning: In y = mx + c, c is the y-intercept. Here c = 13. Final answer: 13. Check: substitute or compare with the original information to confirm the result fits the question.
Tap to mark reviewedGiven information: Rearranging to find gradient/intercept — State the y-intercept of y = 3x + 12. Method choice: use the rearranging to find gradient/intercept method and show each step with the stated values. Calculation or reasoning: In y = mx + c, c is the y-intercept. Here c = 12. Final answer: 12. Check: substitute or compare with the original information to confirm the result fits the question.
Tap to mark reviewedReading coordinates in the wrong order. This is a key trap when answering rearranging to find gradient/intercept questions.
Tap to mark reviewedFor rearranging to find gradient/intercept, show the key representation before the final calculation. Use this final check: Substitute one plotted coordinate into the equation or count a second rise-and-run triangle.
Tap to mark reviewedTravel graphs, Fixed fees and rates
Tap to mark reviewedI can explain rearranging to find gradient/intercept, use the method, check for mistakes, and answer an exam-style question.
Tap to mark reviewedI’m Stuck
Use this whenever a question feels confusing. Nothing here is locked.
Rearranging to find gradient/intercept: Straight-line graphs connect coordinates, rates and equations. Substitute one plotted coordinate into the equation or count a second rise-and-run triangle. Keep the rearranging to find gradient/intercept representation visible until the final line.
Think of rearranging to find gradient/intercept as a careful model: make the important values visible, change one thing at a time, and use the check to prove the answer fits.
Start by naming the given information and the exact result required for rearranging to find gradient/intercept.
Label and read both axes.
Given information: Rearranging to find gradient/intercept — State the y-intercept of y = 3x + 2. Method choice: use the rearranging to find gradient/intercept method and show each step with the stated values. Calculation or reasoning: In y = mx + c, c is the y-intercept. Here c = 2. Final answer: 2. Check: substitute or compare with the original information to confirm the result fits the question.
Method: Label and read both axes. → Plot or identify ordered pairs as x first, then y. → Use rise divided by run for gradient or read the y-axis crossing for intercept. → Check the relationship with a second point or a table value. Record the check explicitly for rearranging to find gradient/intercept.
Reading coordinates in the wrong order. This is a key trap when answering rearranging to find gradient/intercept questions.
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