Maths Library

Slope and linear equations: Grade 9 math

This topic explores linear functions, calculating gradients, and interpreting the equation y = mx + c. The worksheet provides practice in finding slopes, determining intercepts, and sketching or identifying lines.

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What this covers

Slope and linear equations is taught in Grade 9 (age 14 to 15) as a main teaching focus. It sits in the Algebra strand.

Worked example

Find the gradient of the line passing through (1, 3) and (5, 11).

  1. Use the gradient formula: m = (y2 - y1) ÷ (x2 - x1)
  2. Substitute the coordinates: m = (11 - 3) ÷ (5 - 1)
  3. Simplify the fraction: m = 84 = 2

Answer: 2

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Reading the gradient and y-intercept directly from y = mx + c
  2. Calculating positive integer gradients from two coordinates or a drawn line
  3. Calculating negative or fractional gradients and writing equations of lines
  4. Rearranging implicit equations into y = mx + c format, e.g., 2y - 4x = 8
  5. Finding equations of lines parallel or perpendicular to a given line

Common mistakes

  • Inverting the gradient formula to run over rise: (x2 - x1) / (y2 - y1)
  • Misidentifying the gradient when the equation is not written with y as the subject

Curriculum links

Indicative matches to Common Core State Standards. Check wording and codes against the official document.

  • Solve systems of linear equations exactly and approximately using algebraic and graphical methods.
  • Construct linear and exponential functions given a graph, a description of a relationship, or two input-output pairs.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Slope and linear equations

Grade 9 math

Qs
6
Marks
12
NameDateScore / 12
1.
What is the gradient of y = −2x + 4?
[2]
2.
What is the gradient of y = −x + 3?
[2]
3.
What is the gradient of y = −3x − 1?
[2]
4.
What is the gradient of y = x − 2?
[2]
5.
What is the gradient of y = 2x + 3?
[2]
6.
What is the gradient of y = 3x + 1?
[2]

Answer key

  1. −2In y = mx + c the gradient is m, the number in front of x; Gradient = −2
  2. −1In y = mx + c the gradient is m, the number in front of x; Gradient = −1
  3. −3In y = mx + c the gradient is m, the number in front of x; Gradient = −3
  4. 1In y = mx + c the gradient is m, the number in front of x; Gradient = 1
  5. 2In y = mx + c the gradient is m, the number in front of x; Gradient = 2
  6. 3In y = mx + c the gradient is m, the number in front of x; Gradient = 3