Maths Library

Slope and linear equations: Grade 12 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 12 (age 17 to 18) as a topic to introduce. 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.

  • Use straight-line equations, gradients, and criteria for parallel and perpendicular lines to solve coordinate geometry problems.

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 12 math

Qs
6
Marks
24
NameDateScore / 24
1.
Write the equation of the line in the form y = mx + c.
-5-5-4-4-3-3-2-2-1-11122334455
[4]
2.
Write the equation of the line in the form y = mx + c.
-5-5-4-4-3-3-2-2-1-11122334455
[4]
3.
Write the equation of the line in the form y = mx + c.
-5-5-4-4-3-3-2-2-1-11122334455
[4]
4.
Write the equation of the line in the form y = mx + c.
-5-5-4-4-3-3-2-2-1-11122334455
[4]
5.
Write the equation of the line in the form y = mx + c.
-5-5-4-4-3-3-2-2-1-11122334455
[4]
6.
Write the equation of the line in the form y = mx + c.
-5-5-4-4-3-3-2-2-1-11122334455
[4]

Answer key

  1. y = −2x + 4The line crosses the y-axis at 4, so c = 4; It goes −2 up for each 1 across, so m = −2
  2. y = −x + 3The line crosses the y-axis at 3, so c = 3; It goes −1 up for each 1 across, so m = −1
  3. y = −3x − 1The line crosses the y-axis at −1, so c = −1; It goes −3 up for each 1 across, so m = −3
  4. y = x − 2The line crosses the y-axis at −2, so c = −2; It goes 1 up for each 1 across, so m = 1
  5. y = 2x + 3The line crosses the y-axis at 3, so c = 3; It goes 2 up for each 1 across, so m = 2
  6. y = 3x + 1The line crosses the y-axis at 1, so c = 1; It goes 3 up for each 1 across, so m = 3