Gradient, intercept and y = mx + c
Measure how steep a line is with a step triangle, set m and c on sliders, plot a line from a table of values and find the equation of a line through two points.
- UK: Year 9
- France: grade 7
- Germany: grade 8
- Iran: grade 9
- Afghanistan: grade 8
- Syria: grade 9
- Palestine: grade 9
- Ukraine: grade 7
- Russia: grade 7
Guide
The gradient of a line says how steep it is: how far it goes up for every 1 across. Draw a step triangle under the line: across first (the run), then up or down (the rise). Gradient = rise ÷ run. A line that goes down from left to right has a negative gradient, because its rise is negative.
Every straight line (except a vertical one) has an equation y = mx + c. m is the gradient. c is the y-intercept: where the line crosses the y-axis, at the point (0, c). Careful: the y-intercept is on the y-axis, the up-and-down one, not where the line crosses the x-axis.
Before you read a gradient off a grid, look at the numbers on the axes. If one square on the y-axis is 2 units, counting squares gives the wrong rise. Count units, not squares.