š® Algebra Realm Ā· Graphs
Gradient from graph focuses on how to calculate a line's steepness from a drawn graph using a clear slope triangle. In this lesson, focus on straight-line graphs connect coordinates, rates and equations.
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Gradient from graph focuses on how to calculate a line's steepness from a drawn graph using a clear slope triangle. 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 gradient from graph, the final written answer should make that exact relationship visible rather than hiding it inside an unexplained result.
Gradient from graph: 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 gradient from graph 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 gradient from graph.
Substitute one plotted coordinate into the equation or count a second rise-and-run triangle. Write that check beside the final gradient from graph answer.
A rise of 6 over a run of 3 gives gradient 2.
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 gradient from graph.
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: Gradient from graph ā Find the gradient between (2, 6) and (4, 12). Method choice: use the gradient from graph method and show each step with the stated values. Calculation or reasoning: Change in y Ć· change in x = 6 Ć· 2 = 3. Final answer: 3. Check: substitute or compare with the original information to confirm the result fits the question.
Given information: Gradient from graph ā Find the gradient between (14, 42) and (24, 72). Method choice: use the gradient from graph method and show each step with the stated values. Calculation or reasoning: Change in y Ć· change in x = 30 Ć· 10 = 3. Final answer: 3. Check: substitute or compare with the original information to confirm the result fits the question.
Check: Keep the sign: falling left-to-right gives a negative gradient.
Given information: Gradient from graph ā Find the gradient between (13, 39) and (20, 60). Method choice: use the gradient from graph method and show each step with the stated values. Calculation or reasoning: Change in y Ć· change in x = 21 Ć· 7 = 3. Final answer: 3. 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: Gradient from graph ā Find the gradient between (12, 36) and (16, 48). Method choice: use the gradient from graph method and show each step with the stated values. Calculation or reasoning: Change in y Ć· change in x = 12 Ć· 4 = 3. Final answer: 3. 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 gradient from graph answer.
Create a gradient from graph 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 gradient from graph rounds. Solve at least two of three marked rounds and use feedback to correct any error.
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Gradient from graph: 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 gradient from graph representation visible until the final line.
Tap to mark reviewedcoordinate Ā· gradient Ā· y-intercept Ā· axis Ā· linear relationship Ā· graph
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 gradient from graph.
Tap to mark reviewedA rise of 6 over a run of 3 gives gradient 2.
Tap to mark reviewedGiven information: Gradient from graph ā Find the gradient between (2, 6) and (4, 12). Method choice: use the gradient from graph method and show each step with the stated values. Calculation or reasoning: Change in y Ć· change in x = 6 Ć· 2 = 3. Final answer: 3. Check: substitute or compare with the original information to confirm the result fits the question.
Tap to mark reviewedGiven information: Gradient from graph ā Find the gradient between (14, 42) and (24, 72). Method choice: use the gradient from graph method and show each step with the stated values. Calculation or reasoning: Change in y Ć· change in x = 30 Ć· 10 = 3. Final answer: 3. Check: substitute or compare with the original information to confirm the result fits the question.
Tap to mark reviewedGiven information: Gradient from graph ā Find the gradient between (13, 39) and (20, 60). Method choice: use the gradient from graph method and show each step with the stated values. Calculation or reasoning: Change in y Ć· change in x = 21 Ć· 7 = 3. Final answer: 3. Check: substitute or compare with the original information to confirm the result fits the question.
Tap to mark reviewedGiven information: Gradient from graph ā Find the gradient between (12, 36) and (16, 48). Method choice: use the gradient from graph method and show each step with the stated values. Calculation or reasoning: Change in y Ć· change in x = 12 Ć· 4 = 3. Final answer: 3. 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 gradient from graph questions.
Tap to mark reviewedFor gradient from graph, 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 gradient from graph, use the method, check for mistakes, and answer an exam-style question.
Tap to mark reviewedIām Stuck
Use this whenever a question feels confusing. Nothing here is locked.
Gradient from graph: 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 gradient from graph representation visible until the final line.
Think of gradient from graph 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 gradient from graph.
Label and read both axes.
Given information: Gradient from graph ā Find the gradient between (2, 6) and (4, 12). Method choice: use the gradient from graph method and show each step with the stated values. Calculation or reasoning: Change in y Ć· change in x = 6 Ć· 2 = 3. Final answer: 3. Check: substitute or compare with the original information to confirm the result fits the question.
Method: Label and read both axes. ā Plot or identify ordered pairs as x first, then y. ā Use rise divided by run for gradient or read the y-axis crossing for intercept. ā Check the relationship with a second point or a table value. Record the check explicitly for gradient from graph.
Reading coordinates in the wrong order. This is a key trap when answering gradient from graph questions.
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