Gradients and Intercepts of Linear Functions

Gradients and Intercepts of Linear Functions

GCSE(F),

A Linear Function represents a constant rate of change. When plotted on a graph it will be a straight line. A graph may be plotted simply by knowing the gradient and the intercept on the y-axis. The intercept is given by c, and the gradient by m, when the equation of the line is in the form y = mx + c.

Examples

1. Draw a graph for the equation y = 3x + 2

Answer: graph showing intercept of y = -x + 3

Using y = mx + c. c is the intercept = 2 at (0, 2); m is the gradient = 3.

2. Without drawing a graph, determine the coordinates for the intercepts on the x- and y-axes for y + 3x = 12.

Answer: (0, 12) and (4, 0)

When x = 0, then y + 3 x 0 = 12 therefore y = 12 (0, 12).

When y = 0, then 0 + 3x = 12 therefore x = 4 (4, 0).