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Level 5-6 Algebra - Graphs 02

Learn to plot linear relationships in KS3 Maths. Understand gradients, intercepts, and how real-world data forms straight lines on a graph.

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Fascinating Fact:

A phone plan that charges £5 base plus £2 per gigabyte is a line with intercept 5. The point (4, 13) means 4 GB costs £13.

In KS3 Maths, you’ll explore straight-line graphs that show proportional and non-proportional relationships. Each line is defined by an equation in the form y = mx + c, where m is the gradient and c is the y-intercept.

Key Terms

Gradient: The rate of change, showing how steep a line is. It equals rise ÷ run.
Intercept: The point where a line crosses an axis, often the y-intercept at x = 0.
Linear equation: An equation whose graph is a straight line, like y = 2x + 5.

Frequently Asked Questions (Click to see answers)

How can I find the gradient from a graph?

Choose two points on the line, find the difference in y-values and divide by the difference in x-values. Gradient = change in y ÷ change in x.

What does the equation y = mx + c tell us?

It tells us that m is the gradient and c is the y-intercept. The line’s shape and position depend on these two values.

How can I tell if a line is steeper or flatter?

A larger gradient means a steeper line. For example, y = 3x + 1 is steeper than y = x + 1 because 3 > 1.

Try These Related Quizzes

1 .

The following coordinates are at either end of a line drawn on a graph: (-3, 3) and (6, 3). Where does this line appear?

Above the x axis

Below the x axis

Along the x axis

All to the left of the y axis

This is a horizontal line - note that in both sets of coordinates the second numbers are the same

2 .

The following coordinates are at either end of a line drawn on a graph: (-5, -3) and (-5, 8). Where does this line appear?

To the right of the y axis

To the left of the y axis

Along the y axis

All above the x axis

This is a vertical line - note that in both sets of coordinates the first numbers are the same

3 .

The following coordinates are at either end of a line drawn on a graph: (0, -1) and (0, 7). Where does this line appear?

To the right of the y axis

To the left of the y axis

Along the y axis

All above the x axis

Both sets of coordinates show the x axis figure of 0 and this means that the line must run up and down the y axis

4 .

A graph in the form of y = b is what?

A straight horizontal line

A straight vertical line

A left to right diagonal line

A right to left diagonal line

Listen up because this is important....... In the above equation (y = b) the b part of the equation really means anything/something. What you might be asked is something like 'draw the graph y = -2'

5 .

Describe the line y = -2

A horizontal line running two units above the x axis

A horizontal line running two units below the x axis

A vertical line running two units to the left of the y axis

A vertical line running two units to the right of the y axis

Every coordinate on the line would have the structure of (?, -2)

6 .

A graph in the form of x = a is what?

A straight horizontal line

A straight vertical line

A left to right diagonal line

A right to left diagonal line

In the above equation (x = a) the a part of the equation really means anything/something. What you might be asked is something like 'draw the graph x = 4'

7 .

Describe the line x = 4

A horizontal line running four units above the x axis

A horizontal line running four units below the x axis

A vertical line running four units to the left of the y axis

A vertical line running four units to the right of the y axis

Every coordinate on the line would have the structure of (4, ?)

8 .

The graph y = x has a line that goes from where to where?

Quadrant 3 to quadrant 1

Quadrant 3 to quadrant 2

Quadrant 3 to quadrant 4

All the line must be in quadrant 3

Think of it this way: if y = 4 then x = 4, if y = -4 then x = -4. In other words, whatever the first number in the coordinates, the second number will always be the same

9 .

The graph y = -x has a line that goes from where to where?

Quadrant 2 to quadrant 1

Quadrant 2 to quadrant 3

Quadrant 2 to quadrant 4

All the line must be in quadrant 2

Think of it this way: if y = 4 then x = -4, if y = -4 then x = 4. In other words, whatever the first number in the coordinates, the second number will always be the same BUT with the opposite sign

10 .

Which day of the week comes immediately after Monday?

Tuesday

Wednesday

Thursday

Friday

After all that heavy stuff we thought you deserved an easy question!

You can find more about this topic by visiting BBC Bitesize - Graphs

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)