EDGE Math 8

Intercept-Intercept Form

The following is the intercept-intercept form of the equation of a line:

\frac{x}{a} + \frac{y}{b} = 1

where a and b are not equal to 0, and a and b are the x- and y-intercepts of the line, respectively.

Example

Write an equation of the line with –2 as x-intercept and $\frac{1}{2}$ as y-intercept. Express your final answer in general form.

Solution

Using the intercept-intercept form of the equation of the line, where $a = - 2$ and $b = \frac{1}{2},$ you will get:

\begin{array}{l} \frac{x}{- 2} + \frac{y}{\frac{1}{2}} = 1 \\ \frac{x}{- 2} + \frac{2 y}{1} = 1 \\ x - 4 y = - 2 \\ x - 4 y + 2 = 0 \end{array}