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* = m*x* + c.

## Examples

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

Answer:

Using *y* = m*x* + 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* + 3*x* = 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 + 3*x* = 12 therefore *x* = 4 (4, 0).

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