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Maths Gcse Edexcel Higher

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  1. Scatter-Graphs-And-Correlation Edexcel Higher
    2 主题
  2. Cumulative-Frequency-And-Box-Plots Edexcel Higher
    4 主题
  3. Histograms Edexcel Higher
    3 主题
  4. Statistical-Diagrams Edexcel Higher
    7 主题
  5. Averages-Ranges-And-Data Edexcel Higher
    8 主题
  6. Combined-And-Conditional-Probability Edexcel Higher
    3 主题
  7. Tree-Diagrams Edexcel Higher
    1 主题
  8. Simple-Probability-Diagrams Edexcel Higher
    3 主题
  9. Transformations Edexcel Higher
    5 主题
  10. Vectors Edexcel Higher
    6 主题
  11. 3D-Pythagoras-And-Trigonometry Edexcel Higher
    1 主题
  12. Sine-Cosine-Rule-And-Area-Of-Triangles Edexcel Higher
    4 主题
  13. Pythagoras-And-Trigonometry Edexcel Higher
    4 主题
  14. Area-And-Volume-Of-Similar-Shapes Edexcel Higher
    1 主题
  15. Congruence-Similarity-And-Geometrical-Proof Edexcel Higher
    5 主题
  16. Volume-And-Surface-Area Edexcel Higher
    3 主题
  17. Circles-Arcs-And-Sectors Edexcel Higher
    2 主题
  18. Area-And-Perimeter Edexcel Higher
    4 主题
  19. Circle-Theorems Edexcel Higher
    7 主题
  20. Bearings-Scale-Drawing-Constructions-And-Loci Edexcel Higher
    5 主题
  21. Angles-In-Polygons-And-Parallel-Lines Edexcel Higher
    3 主题
  22. Symmetry-And-Shapes Edexcel Higher
    6 主题
  23. Exchange-Rates-And-Best-Buys Edexcel Higher
    2 主题
  24. Standard-And-Compound-Units Edexcel Higher
    5 主题
  25. Direct-And-Inverse-Proportion Edexcel Higher
    2 主题
  26. Problem-Solving-With-Ratios Edexcel Higher
    2 主题
  27. Ratios Edexcel Higher
    3 主题
  28. Sequences Edexcel Higher
    4 主题
  29. Transformations-Of-Graphs Edexcel Higher
    2 主题
  30. Graphing-Inequalities Edexcel Higher
    2 主题
  31. Solving-Inequalities Edexcel Higher
    2 主题
  32. Real-Life-Graphs Edexcel Higher
    4 主题
  33. Estimating-Gradients-And-Areas-Under-Graphs Edexcel Higher
    2 主题
  34. Equation-Of-A-Circle Edexcel Higher
    2 主题
  35. Graphs-Of-Functions Edexcel Higher
    6 主题
  36. Linear-Graphs Edexcel Higher
    4 主题
  37. Coordinate-Geometry Edexcel Higher
    4 主题
  38. Functions Edexcel Higher
    3 主题
  39. Forming-And-Solving-Equations Edexcel Higher
    3 主题
  40. Iteration Edexcel Higher
    1 主题
  41. Simultaneous-Equations Edexcel Higher
    2 主题
  42. Quadratic-Equations Edexcel Higher
    4 主题
  43. Linear-Equations Edexcel Higher
    1 主题
  44. Algebraic-Proof Edexcel Higher
    1 主题
  45. Rearranging-Formulas Edexcel Higher
    2 主题
  46. Algebraic-Fractions Edexcel Higher
    4 主题
  47. Completing-The-Square Edexcel Higher
    1 主题
  48. Factorising Edexcel Higher
    6 主题
  49. Expanding-Brackets Edexcel Higher
    3 主题
  50. Algebraic-Roots-And-Indices Edexcel Higher
    1 主题
  51. Introduction Edexcel Higher
    7 主题
  52. Using-A-Calculator Edexcel Higher
    1 主题
  53. Surds Edexcel Higher
    2 主题
  54. Rounding-Estimation-And-Bounds Edexcel Higher
    2 主题
  55. Fractions-Decimals-And-Percentages Edexcel Higher
    3 主题
  56. Simple-And-Compound-Interest-Growth-And-Decay Edexcel Higher
    4 主题
  57. Percentages Edexcel Higher
    3 主题
  58. Fractions Edexcel Higher
    4 主题
  59. Powers-Roots-And-Standard-Form Edexcel Higher
    4 主题
  60. Prime-Factors-Hcf-And-Lcm Edexcel Higher
    4 主题
  61. Number-Operations Edexcel Higher
    10 主题
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Exam code:1MA1

Finding equations of straight lines

What is the equation of a straight line?

  • The general equation of a straight line is y = mx + c where

    • m is the gradient

    • c  is the y-intercept

      • The value where it cuts the y-axis

  • y = 5x + 2 is a straight line with

    • gradient 5

    • y-intercept 2

  • y = 3 – 4x is a straight line with

    • gradient -4

    • y-intercept 3

How do I find the equation of a straight line from a graph?

  • Find the gradient by drawing a triangle and using

    • gradient equals rise over run

      • Positive for uphill lines, negative for downhill

  • Read off the y-intercept from the graph

    • Where it cuts the y-axis

  • Substitute these values into y = mx + c 

What if no y-intercept is shown?

  • If you can’t read off the y-intercept

    • find any point on the line

    • substitute it into the equation

    • solve to find c 

  • For example, a line with gradient 6 passes through (2, 15)

    • The y-intercept is unknown

      • Write y = 6x + c

    • Substitute in x = 2 and y = 15

      • 15 = 6 × 2 + c

      • 15 = 12 + c

    • Solve for c

      • c  = 3

    • The equation is y  = 6x + 3

What are the equations of horizontal and vertical lines?

  • A horizontal line has the equation y = c

    • c is the y-intercept

  • A vertical line has the equation x  = k

    •  k is the x-intercept

  • For example

    • y = 4

    • x = -2

Worked Example

(a) Find the equation of the straight line shown in the diagram below.

Graph of a straight line with negative gradient

Find m, the gradient
Identify any two points the line passes through and work out the rise and run

Line passes through (2, 4) and (10, 0)

Finding the equation of a straight line from a graph

The rise is 4
The run is 8

Calculate the fraction rise over run

rise over run equals 4 over 8 equals 1 half

The slope is downward (downhill), so it is a negative gradient

gradient, <img alt=”m equals negative 1 half” data-mathml='<math ><semantics><mrow><mi >m</mi><mo >=</mo><mo >-</mo><mfrac ><mn>1</mn><mn>2</mn></mfrac></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true}</annotation></semantics></math>’ data-type=”working” height=”47″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2247%22%20width%3D%2267%22%20wrs%3Abaseline%3D%2230%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%20mathcolor%3D%22%23000000%22%3Em%3C%2Fmi%3E%3Cmo%20mathcolor%3D%22%23000000%22%3E%3D%3C%2Fmo%3E%3Cmo%20mathcolor%3D%22%23000000%22%3E-%3C%2Fmo%3E%3Cmfrac%20mathcolor%3D%22%23000000%22%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math143f4d31b04031e49f5eb18baba’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADxjdnQgDVUNBwAAAVgAAAA6Z2x5ZoPi2VsAAAGUAAAA%2FGhlYWQQC2qxAAACkAAAADZoaGVhCGsXSAAAAsgAAAAkaG10eE2rRkcAAALsAAAADGxvY2EAHTwYAAAC%2BAAAABBtYXhwBT0FPgAAAwgAAAAgbmFtZaBxlY4AAAMoAAABn3Bvc3QB9wD6AAAEyAAAACBwcmVwa1uragAABOgAAAAUAAADSwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg1UADev96AAAD6ACWAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACgAAAAGAAQAAQACAD0iEv%2F%2FAAAAPSIS%2F%2F%2F%2FxN3wAAEAAAAAAAAAAAFUAywAgAEAAFYAKgJYAh4BDgEsAiwAWgGAAoAAoADUAIAAAAAAAAAAKwBVAIAAqwDVAQABKwAHAAAAAgBVAAADAAOrAAMABwAAMxEhESUhESFVAqv9qwIA%2FgADq%2FxVVQMAAAIAgADrAtUCFQADAAcAZRgBsAgQsAbUsAYQsAXUsAgQsAHUsAEQsADUsAYQsAc8sAUQsAQ8sAEQsAI8sAAQsAM8ALAIELAG1LAGELAH1LAHELAB1LABELAC1LAGELAFPLAHELAEPLABELAAPLACELADPDEwEyE1IR0BITWAAlX9qwJVAcBV1VVVAAEAgAFVAtUBqwADADAYAbAEELEAA%2FawAzyxAgf1sAE8sQUD5gCxAAATELEABuWxAAETELABPLEDBfWwAjwTIRUhgAJV%2FasBq1YAAQAAAAEAANV4zkFfDzz1AAMEAP%2F%2F%2F%2F%2FWOhNz%2F%2F%2F%2F%2F9Y6E3MAAP8gBIADqwAAAAoAAgABAAAAAAABAAAD6P9qAAAXcAAA%2F7YEgAABAAAAAAAAAAAAAAAAAAAAAwNSAFUDVgCAA1YAgAAAAAAAAAAoAAAAsgAAAPwAAQAAAAMAXgAFAAAAAAACAIAEAAAAAAAEAADeAAAAAAAAABUBAgAAAAAAAAABABIAAAAAAAAAAAACAA4AE

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