Question

Find the slope and the y-intercept of the line with the equation 9y - 6x + 8 = 0.Select the correct choice below and fill in any answer boxes within your choice. A. The slope is(Type an integer or a simplified fraction.)B. The slope is undefined.Select the correct choice below and fill in any answer boxes within your choice.A. The y-intercept is(Type an integer or a simplified fraction. Type an ordered pair.)B. There is no y intercept

Answer 1

Rewrite the given equation in slope intercept form, y=mx+c. Where the slope is m and the y-intercept is c.

Rewrite the given equation as follows:

$\begin{gathered} 9y-6x+8=0 \\ \text{Take x term and the constant to the right side and change their sign} \\ 9y=6x-8 \\ \text{Divide each term by 9:} \\ \frac{9y}{9}=\frac{6x}{9}-\frac{8}{9} \end{gathered}$

Simplify the equation:

$y=\frac{6}{9}x-\frac{8}{9}$

Compare to the equation y=mx+c, to get:

$\begin{gathered} m=\frac{6}{9} \\ c=-\frac{8}{9} \end{gathered}$

Hence, the slope is 6/9 and the y-intercept is -8/9.

You can also write the y-intercept as an ordered pair (0,-8/9) since the x-value at the y-intercept is zero.