Graphs & Sequences

Straight-line graphs (y = mx + c), nth term of sequences, and an introduction to quadratic graphs.

You must be able to draw and interpret linear graphs and find the nth term of sequences. Higher tier also requires quadratic graphs.

Straight-line graphs y = mx + c

m = gradient (steepness) c = y-intercept (where the line crosses the y-axis) Gradient = (change in y) / (change in x)

Worked example

A line passes through (0, 3) and (4, 11). Find its equation.

Solution

Gradient m = (11−3)/(4−0) = 8/4 = 2 y-intercept c = 3 **y = 2x + 3**

For a sequence with common difference d: nth term = dn + (first term − d) Or: find the difference, write dn, then adjust the constant.

Worked example

Find the nth term of: 5, 8, 11, 14, …

Solution

Common difference = 3 3n sequence: 3, 6, 9, 12, … Our sequence is 2 more: **3n + 2**

Try these without looking at the answers first.

Q1.Find the equation of the line through (0, −1) and (2, 5).

Show answer

y = 3x − 1

Q2.nth term of 4, 7, 10, 13, …?

Show answer

3n + 1

Q3.nth term of 2, 6, 10, 14, …?

Show answer

4n − 2