Straight-line graphs · Grade 8
In Grade 8 you learn: plotting straight lines from a table; gradient and y-intercept; y = mx + c.
Every straight line can be written as y = mx + c. The gradient m says how steep the line is, and c says where it crosses the y-axis. Straight lines model anything that changes at a steady rate, such as a phone bill or a taxi fare.
Key facts
- In y = mx + c, m is the gradient and c is the y-intercept.
- Gradient = change in y ÷ change in x (“rise over run”).
- A positive gradient slopes up to the right; a negative gradient slopes down.
- Parallel lines have the same gradient.
- For the line through two points: find m, then substitute one point into y = mx + c to find c.
Worked examples
Example 1
Find the gradient and y-intercept of 2y = 6x − 8.
Answer: Gradient 3, y-intercept −4
Example 2
Find the equation of the line through (1, 5) and (4, 11).
Answer: y = 2x + 3