Straight-line graphs GCSE lesson: gradient and intercept, y = mx + c

Straight lines: practice

Show your working on paper. Write negative numbers with a minus sign. The stretch is optional.

Diagnostic question: choose and explain

1. y = 3 − 2x. What are its gradient m and its y-intercept c?
   1. m = −2, c = 3
   2. m = 3, c = −2
   3. m = 2, c = 3
   4. m = 3, c = 2

Practice questions

1. y = 4x − 3 has gradient ___ and y-intercept ___
2. y = 6 − x. What is its gradient?
3. A line goes through (0, 2) and (2, 8). What is its gradient?
4. 2y = 8x + 2. What is the gradient of this line?
5. Which line is parallel to y = 2x + 1?
   1. y = x + 2
   2. y = 2x − 5
   3. y = −2x + 1
   4. y = 3x + 1
6. Is the point (3, 7) on the line y = 2x + 1?
   1. Yes
   2. No
7. y = 2x + 1 meets the x-axis where y = 0, at x = ___
8. The line y = mx + 1 goes through (2, 7). What is m?
9. Which line is steeper: y = −4x or y = 3x?
   1. y = −4x
   2. y = 3x
   3. They are equally steep
10. Stretch: the line through (1, 5) and (3, 1) is y = ___x + ___

Support: For question 3: count up from y = 2 to y = 8, then across from x = 0 to x = 2. The gradient is up ÷ across. The line crosses the y-axis where x = 0.

Straight lines: exit

One or two sentences are enough.

1. Write the equation of a line that is steeper than y = 2x + 1 and crosses the y-axis at the same point. Say how you know.

Exit check

Three sketches and one sentence show who sees what m and c each do.

Sketch y = 2x + 1, then a line parallel to it, then a line that goes down and crosses the y-axis at 1. Label where each crosses the y-axis.

Straight lines: read, find and sketch

Show your working. For question 3, find the gradient as up ÷ across, then put a point in to find c. Check each equation with a point.