Watch out
Mixing up x and y coordinates.
Back to National 5 Mathematics
SQA National 5 Mathematics
Straight line graphs
Using y = mx + c and plotting straight lines.
Formula reference
Check the National 5 rules and formulae linked to this topic.
Which method?
Match exam clues to a suitable method.
Before you start
- Know that straight lines have constant gradient.
- Read coordinates as (x, y).
- Remember y = mx + c.
Explanation
A straight line graph can be described by an equation such as y = 2x + 1.
The coefficient of x is the gradient, which tells you how steep the line is. The constant term is the y-intercept.
To draw a line, plot two or more points that satisfy the equation and join them with a straight line.
Visual support
Coordinate grid and gradient
Key formulae and rules
- y = mx + c
- m = change in y / change in x
Check
Use one coordinate from the graph in your equation. The left and right sides should match.
Exam tip
For graph questions, a table of values is often the simplest way to avoid plotting errors.
Calculator tip
Use brackets for fractions, powers and square roots, then round only at the final line.
Worked examples
Worked example 1
Plot a straight line
Draw y = 2x + 1 for x = −1, 0, 1, 2
- When x = −1, y = −1
- When x = 0, y = 1
- When x = 1, y = 3
- When x = 2, y = 5
Answer: Plot (-1, −1), (0, 1), (1, 3), (2, 5) and join them.
Worked example 2
Find an equation from the graph
A line crosses the y-axis at 3 and rises 2 for every 1 across.
- The y-intercept is c = 3.
- The gradient is m = 2.
- Substitute into y = mx + c
So: The equation is y = 2x + 3.
Worked example 3
Check if a point lies on a line
Does (4, 11) lie on y = 3x − 1?
- Substitute x = 4 into y = 3x − 1
- y = 3(4) − 1 = 11
- This matches the y-coordinate.
Answer: Yes, (4, 11) lies on the line.
Watch out
- Mixing up x and y coordinates.
- Using the intercept as the gradient.
- Drawing a line through points that do not satisfy the equation.