Sure! Let's convert the given equation of the line from its standard form to slope-intercept form.
### Given Equation:
[tex]\[ 9x + 3y = -9 \][/tex]
The goal is to rewrite this equation in the slope-intercept form, which is:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
#### Step-by-Step Solution:
1. Start with the original equation:
[tex]\[ 9x + 3y = -9 \][/tex]
2. Isolate the [tex]\( y \)[/tex]-term:
To do this, we need to move the [tex]\( 9x \)[/tex] term to the right side of the equation:
[tex]\[ 3y = -9 - 9x \][/tex]
3. Simplify the right side:
You can rewrite [tex]\( -9 - 9x \)[/tex] as:
[tex]\[ 3y = -9x - 9 \][/tex]
4. Divide every term by 3 to solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{-9x}{3} + \frac{-9}{3} \][/tex]
5. Simplify the fractions:
[tex]\[ y = -3x - 3 \][/tex]
Therefore, the equation [tex]\( 9x + 3y = -9 \)[/tex] in slope-intercept form [tex]\( y = mx + b \)[/tex] is:
[tex]\[ y = -3x - 3 \][/tex]
So, the slope-intercept form of the given equation is:
[tex]\[ \boxed{y = -3x - 3} \][/tex]
This represents the same line, now expressed where the slope ([tex]\( m \)[/tex]) is [tex]\(-3\)[/tex] and the y-intercept ([tex]\( b \)[/tex]) is [tex]\(-3\)[/tex].
