To put the equation [tex]\( 9x + 3y = -9 \)[/tex] into slope-intercept form [tex]\( y = mx + b \)[/tex], you will follow these steps:
1. Isolate the Term with [tex]\( y \)[/tex]: Start by isolating the term that contains [tex]\( y \)[/tex] on one side of the equation. You can do this by subtracting [tex]\( 9x \)[/tex] from both sides of the equation.
[tex]\[
9x + 3y - 9x = -9 - 9x
\][/tex]
Simplifying, you get:
[tex]\[
3y = -9x - 9
\][/tex]
2. Solve for [tex]\( y \)[/tex]: Next, solve for [tex]\( y \)[/tex] by dividing every term in the equation by the coefficient of [tex]\( y \)[/tex], which is 3.
[tex]\[
\frac{3y}{3} = \frac{-9x - 9}{3}
\][/tex]
Simplifying, you get:
[tex]\[
y = -3x - 3
\][/tex]
The slope-intercept form of the equation [tex]\( 9x + 3y = -9 \)[/tex] is [tex]\( y = -3x - 3 \)[/tex], where the slope [tex]\( m \)[/tex] is -3, and the y-intercept [tex]\( b \)[/tex] is -3.
