ax + by + c = 0

This equation is used to avoid fractions.

It can make the equation of a line look “tidier”.

a, b & c are all integers and usually a > 0.

eg 5x - 4y + 7 = 0

Note: Integers = {….-2, -1, 0, 1, 2, …..}

An alternative for the equation of a straight line is given by:

Example 1: (y = mx + c ax + by + c = 0)

Suppose that y = -3/5x + 2/3

Example 2: (ax + by + c = 0 y = mx + c)

X 15

We now get 15y = -9x + 10 Move all to left

This becomes 9x + 15y - 10 = 0

Find the gradient & intercept for 6x + 3y - 16 = 0

Starting with 6x + 3y - 16 = 0 (-6x & +16)We now get 3y = -6x + 16 3Finally we have y = -2x + 16/3

This line has gradient -2 and intercept (0, 16/3)

Example 3 Prove that the line meeting the X-axis at 63.43° is

parallel to 10x - 5y + 7 = 0.

Line 1

m = tan m = tan 63.43°

m = 2

Line 2

10x - 5y + 7 = 0

10x + 7 = 5y

y = 2x + 7/5

m=2

Lines have same gradient so must be parallel.