Forming equations of given straight line graph (using y=mx+c)

Form the equation of a supplied non-vertical straight-line graph in the form y = mx + c by reading or calculating its gradient and y-intercept.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • NA5-9
New NZC (2026)
  • NZC26-P4-ALG-ER-K-Y9-05
  • NZC26-P4-ALG-ER-P-Y10-06
  • NZC26-P4-ALG-ER-K-Y10-08
  • NZC26-P4-ALG-ER-P-Y10-05
  • NZC26-P4-ALG-ER-P-Y10-08

Resources

  • CorbettMaths on y=mx+cQuestions PDF · Answers
  • Beta: Plotting co-ordinates, Ex 13.01, pgs 230 & 231
  • Beta: Drawing line from equation, Ex 13.02, pg 233
  • Beta: Gradients, Ex 13.03 to Ex 13.06, pgs 235 & 239
  • Beta: Intercept of lines, Ex 13.07 to Ex 13.08, pgs 240 & 241
  • Beta: Horizontal and vertical lines, Ex 13.09, pg 243
  • Beta: Applying straight-line rules, Ex 13.10, pgs 244 to 246
  • Dr Austin Maths - Finding Equations of Straight Lines from Graphs Practice GridQuestions PDF · Answers
  • Dr Austin Maths - Finding Harder Equations of Straight Lines from Graphs Practice GridQuestions PDF · Answers
  • Dr Austin Maths - Equation of a Straight Line Revision Practice GridQuestions PDF · Answers

Terminology

  • Equation of a line
  • Gradient
  • Slope
  • y-intercept
  • y = mx + c
  • m (gradient coefficient)
  • c (y-intercept constant)
  • Linear equation
  • Rise and run
  • Positive gradient
  • Negative gradient
  • Horizontal line

Task goals

  • Form the equation of a straight line using the formula $y = mx + c$ when given the gradient and y-intercept.
  • Identify gradient $m$ and y-intercept $c$ from a line on a graph and use these to write the equation.
  • Use the y-axis crossing point and rise-over-run to determine both parameters in $y = mx + c$.
  • Write equations for lines with integer and fractional gradients, including negative gradients.
  • Apply the equation form to predict values and understand the behaviour of linear relationships.

Where this fits

What leads into this objective, and where it goes next.

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Forming equations of given straight line graph (using y=mx+c)

Forming equations of given straight line graph (using y=mx+c)

Know

For a specific straight line, the gradient, m, and y-intercept, c, are fixed, and x varies with y according to the rule y = mx + c.

Statement▸
Year 9 · Algebra · Equations and relationships
NZC26-P4-ALG-ER-K-Y9-05

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