🔮 Algebra Realm · Graphs
Testing if points lie on a line focuses on how to check whether a coordinate satisfies a line equation by substitution. In this lesson, focus on straight-line graphs connect coordinates, rates and equations.
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Level 1 · Apprentice0 / 100 XP
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Testing if points lie on a line focuses on how to check whether a coordinate satisfies a line equation by substitution. 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 testing if points lie on a line, the final written answer should make that exact relationship visible rather than hiding it inside an unexplained result.
Testing if points lie on a line: 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 testing if points lie on a line 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 testing if points lie on a line.
Substitute one plotted coordinate into the equation or count a second rise-and-run triangle. Write that check beside the final testing if points lie on a line answer.
(2, 5) lies on y = 2x + 1 because 2(2) + 1 = 5.
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 testing if points lie on a line.
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: Testing if points lie on a line — Does (2, 8) lie on y = 3x + 2? Method choice: use the testing if points lie on a line method and show each step with the stated values. Calculation or reasoning: Substitute x = 2: 3 × 2 + 2 = 8. This matches the point's y-value 8, so Final answer: yes. Check: substitute or compare with the original information to confirm the result fits the question.
Given information: Testing if points lie on a line — Does (10, 46) lie on y = 3x + 14? Method choice: use the testing if points lie on a line method and show each step with the stated values. Calculation or reasoning: Substitute x = 10: 3 × 10 + 14 = 44. This does not match the point's y-value 46, so Final answer: no. Check: substitute or compare with the original information to confirm the result fits the question.
Check: Compare with the point's stated y-coordinate.
Given information: Testing if points lie on a line — Does (7, 34) lie on y = 3x + 13? Method choice: use the testing if points lie on a line method and show each step with the stated values. Calculation or reasoning: Substitute x = 7: 3 × 7 + 13 = 34. This matches the point's y-value 34, so Final answer: yes. 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: Testing if points lie on a line — Does (4, 26) lie on y = 3x + 12? Method choice: use the testing if points lie on a line method and show each step with the stated values. Calculation or reasoning: Substitute x = 4: 3 × 4 + 12 = 24. This does not match the point's y-value 26, so Final answer: no. 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 testing if points lie on a line answer.
Create a testing if points lie on a line 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 testing if points lie on a line rounds. Solve at least two of three marked rounds and use feedback to correct any error.
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Testing if points lie on a line: 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 testing if points lie on a line representation visible until the final line.
Tap to mark reviewedcoordinate · gradient · y-intercept · axis · linear relationship · testing · if
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 testing if points lie on a line.
Tap to mark reviewed(2, 5) lies on y = 2x + 1 because 2(2) + 1 = 5.
Tap to mark reviewedGiven information: Testing if points lie on a line — Does (2, 8) lie on y = 3x + 2? Method choice: use the testing if points lie on a line method and show each step with the stated values. Calculation or reasoning: Substitute x = 2: 3 × 2 + 2 = 8. This matches the point's y-value 8, so Final answer: yes. Check: substitute or compare with the original information to confirm the result fits the question.
Tap to mark reviewedGiven information: Testing if points lie on a line — Does (10, 46) lie on y = 3x + 14? Method choice: use the testing if points lie on a line method and show each step with the stated values. Calculation or reasoning: Substitute x = 10: 3 × 10 + 14 = 44. This does not match the point's y-value 46, so Final answer: no. Check: substitute or compare with the original information to confirm the result fits the question.
Tap to mark reviewedGiven information: Testing if points lie on a line — Does (7, 34) lie on y = 3x + 13? Method choice: use the testing if points lie on a line method and show each step with the stated values. Calculation or reasoning: Substitute x = 7: 3 × 7 + 13 = 34. This matches the point's y-value 34, so Final answer: yes. Check: substitute or compare with the original information to confirm the result fits the question.
Tap to mark reviewedGiven information: Testing if points lie on a line — Does (4, 26) lie on y = 3x + 12? Method choice: use the testing if points lie on a line method and show each step with the stated values. Calculation or reasoning: Substitute x = 4: 3 × 4 + 12 = 24. This does not match the point's y-value 26, so Final answer: no. 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 testing if points lie on a line questions.
Tap to mark reviewedFor testing if points lie on a line, 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 testing if points lie on a line, 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.
Testing if points lie on a line: 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 testing if points lie on a line representation visible until the final line.
Think of testing if points lie on a line 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 testing if points lie on a line.
Label and read both axes.
Given information: Testing if points lie on a line — Does (2, 8) lie on y = 3x + 2? Method choice: use the testing if points lie on a line method and show each step with the stated values. Calculation or reasoning: Substitute x = 2: 3 × 2 + 2 = 8. This matches the point's y-value 8, so Final answer: yes. 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 testing if points lie on a line.
Reading coordinates in the wrong order. This is a key trap when answering testing if points lie on a line questions.
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