A10AlgebraFoundation & Higher

Straight Line Graphs

Every straight line has an equation in the form $y = m x + c$ . Once you understand what $m$ and $c$ mean, you can draw any line and read its equation straight off a graph.

45 min Video by Maths Genie AQA GCSE Maths

Drawing Straight Line GraphsWatch the walkthrough, then read the notes below.

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What you'll learn

Plot a straight line from its equation
Find the gradient of a line
Identify the y-intercept
Write the equation y = mx + c

y = mx + c

In $y = m x + c$ , $m$ is the $gradient$ (how steep the line is) and $c$ is the $y-intercept$ (where it crosses the y-axis). A positive gradient slopes up; a negative one slopes down.

y = m x + c

m = gradient, c = y-intercept.

Finding the gradient

Gradient is “rise over run” — how much the line goes up divided by how much it goes across between two points.

m = \frac{change in y}{change in x}

Rise over run.

1Gradient

= \frac{7 - 1}{2 - 0} = 3

2It crosses the y-axis at 1, so

c = 1

Answer

y = 3 x + 1

Tip — Parallel lines have the same gradient (the same value of m).

Remember these

y = m x + c

Equation of a straight line.

m = \frac{Δ y}{Δ x}

Gradient = rise ÷ run.

Watch out for these

Reading the gradient and intercept the wrong way round.

m (with the x) is the gradient; c (on its own) is the y-intercept.

Calculating run over rise.

Gradient is rise over run: change in y ÷ change in x.

Key takeaways

Straight line: y = mx + c.
m = gradient (rise over run), c = y-intercept.
Parallel lines share the same gradient.

Test yourself

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