EDGE Math 8

Example 1

Write the equation $12 x - 4 y = 96$ in slope-intercept form. Identify the slope and the y-intercept of the line.

Solution

Solving for y in the equation $12 x - 4 y = 96,$ you will get:

\begin{array}{l} 12 x - 4 y = 96 \\ - 4 y = - 12 x + 96 \\ y = \frac{- 12}{- 4} x + \frac{96}{- 4} \\ y = 3 x - 24. \end{array}

The slope of the line having the equation $y = 3 x - 24$ is 3 and its y-intercept is –24.

Example 2

Write an equation of the line whose y-intercept is $\frac{3}{5}$ and slope is $\frac{- 9}{2} .$ Express your final answer in general form.

Solution

Using the slope-intercept form of the equation of a line with $m = \frac{- 9}{2}$ and $b = \frac{3}{5},$ you will get:

\begin{array}{l} y = \frac{- 9}{2} x + \frac{3}{5} \\ 10 y = 10 (\frac{- 9}{2} x + \frac{3}{5}) \\ 10 y = 5 (- 9 x) + 2 (3) \\ 10 y = - 45 x + 6 \end{array}

Writing the last equation in general form gives you:

45 x + 10 y - 6 = 0.