Watch out
Doing change in x divided by change in y.
Back to National 5 Mathematics
SQA National 5 Mathematics
Gradient and intercept
Finding and interpreting gradient and y-intercept.
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
- Read two coordinates accurately.
- Know vertical change is change in y.
- Know horizontal change is change in x.
Explanation
The gradient measures steepness. It is calculated by dividing the change in y by the change in x.
The y-intercept is where the line crosses the y-axis, so x = 0 at that point.
In y = mx + c, m is the gradient and c is the y-intercept
Visual support
Coordinate grid and gradient
Key formulae and rules
- gradient = (y2 − y1) / (x2 − x1)
- y = mx + c
Check
Use one coordinate from the graph in your equation. The left and right sides should match.
Exam tip
Write the gradient fraction before simplifying; this shows the method clearly.
Calculator tip
Use brackets for fractions, powers and square roots, then round only at the final line.
Worked examples
Worked example 1
Find a gradient
Find the gradient of the line through (2, 3) and (6, 11).
- Change in y = 11 − 3 = 8
- Change in x = 6 − 2 = 4
- Gradient = 8 / 4 = 2.
Answer: The gradient is 2.
Worked example 2
Find the intercept
A line has equation y = −4x + 7. State the gradient and y-intercept.
- Compare with y = mx + c
- m = −4
- c = 7
So: Gradient −4, y-intercept 7.
Worked example 3
Find the equation
A line has gradient 3 and passes through (0, −2).
- The y-intercept is −2 because x = 0.
- Use y = mx + c.
- m = 3 and c = −2
Answer: The equation is y = 3x − 2.
Watch out
- Doing change in x divided by change in y.
- Ignoring a negative gradient.
- Thinking the x-intercept is c.