5.1PureFoundation

y = mx + c

Every straight line can be written as $y = m x + c$ , where $m$ is the gradient and $c$ is the $y$ -intercept. These two numbers tell you everything about the line — its steepness and where it crosses the $y$ -axis.

25 min Video by Zeeshan Zamurred Straight Line Graphs

Edexcel Straight Lines — full chapter playlist (Zeeshan Zamurred)Watch the full walkthrough before the notes below.

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What you'll be able to do

Identify the gradient and intercept from y = mx + c
Calculate a gradient from two points
Sketch a line from its equation
Rearrange a linear equation into y = mx + c form

Gradient and intercept

In $y = m x + c$ , the coefficient $m$ is the $gradient$ (how steep) and $c$ is the $y-intercept$ (where it crosses the $y$ -axis).

y = m x + c

m

= gradient,

c

y

-intercept.

m = 3

c = - 2

Answergradient 3, intercept

- 2

Gradient from two points

The gradient between two points is the change in $y$ over the change in $x$ .

m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

Rise over run.

\frac{11 - 2}{4 - 1} = \frac{9}{3}

Answer

3

Tip — Keep the points in the same order top and bottom: (y₂ − y₁) over (x₂ − x₁).

Rearranging into the form

Equations are not always given as $y = m x + c$ . Rearrange to make $y$ the subject so you can read off $m$ and $c$ .

1Rearrange:

y = - 2 x + 5

Answergradient

- 2

Formula recap

y = m x + c

Gradient-intercept form.

m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

Gradient from two points.

Common mistakes to avoid

Reading the gradient off before rearranging to y = ….

Make y the subject first, then m is the coefficient of x.

Calculating the gradient as Δx/Δy.

It is Δy/Δx — rise over run.

Key takeaways

y = mx + c: m is the gradient, c is the y-intercept.
Gradient between points = (y₂ − y₁)/(x₂ − x₁).
Rearrange to y = … before reading off m and c.

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