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C3.3 Gradient of linear graphs

Syllabus
0580–2028–2029
Topic
C3.3
Level
Core

Find a straight line’s gradient from a grid

The gradient measures how much a straight line changes vertically for each horizontal change. Read both changes from two clear points on the grid.

gradient=vertical changehorizontal change=y2−y1x2−x1\text{gradient}=\frac{\text{vertical change}}{\text{horizontal change}}=\frac{y_2-y_1}{x_2-x_1}

Choose two well-separated points that lie exactly on the line, preferably grid intersections; read each axis scale; move from the left point to the right point; record the signed vertical change and the positive horizontal change; divide and simplify.

A(−2,4), B(4,1):gradient=1−44−(−2)=−36=−12A(-2,4),\ B(4,1):\qquad \text{gradient}=\frac{1-4}{4-(-2)}=\frac{-3}{6}=-\frac12

Line direction from left to right Gradient
rises positive
falls negative
horizontal 00
vertical undefined because horizontal change is 00

A larger triangle usually makes grid readings more reliable. Using any other pair of exact points on the same straight line must give the same ratio.

For Core C3.3, obtain the gradient from the grid. Do not count squares without checking the axis scales, and do not discard the negative sign when the line falls from left to right.