Rearranging an equation

To determine the and y-intercept from an equation of a straight line which is not in the correct form, we will need to rearrange the equation first.

Find the gradient and y-intercept for the straight line with equation \(2x + y - 13 = 0\).

Rearrange the equation into the form \(y = mx + c\) using the algebraic rules for solving equations.

\(2x + y - 13 = 0\)

\(2x + y = 0 + 13\)

\(y = 13 - 2x\)

\(y = - 2x + 13\)

Therefore the gradient \(m = - 2\)

and the y-intercept: \(c = 13\, \to (0,13)\)

Now try the example question below.

Question

Find the gradient of the line with equation \(2x + 5y - 6 = 0\)

Find the gradient and y-intercept for the straight line with equation:

\(2y - 5x = 12\).