To convert the given equation [tex]\(2x + 2y = -16\)[/tex] into slope-intercept form, we need to solve for [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex]. The slope-intercept form of a line is given by [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept.
Here are the steps to convert and simplify the given equation:
1. Start with the given equation:
[tex]\[
2x + 2y = -16
\][/tex]
2. Isolate the [tex]\(y\)[/tex]-term on one side of the equation. To do this, first subtract [tex]\(2x\)[/tex] from both sides:
[tex]\[
2y = -2x - 16
\][/tex]
3. Solve for [tex]\(y\)[/tex] by dividing every term by 2. This will isolate [tex]\(y\)[/tex] on the left side of the equation:
[tex]\[
y = \frac{-2x - 16}{2}
\][/tex]
4. Simplify each term in the resulting equation. Divide each term in the numerator by 2:
[tex]\[
y = \frac{-2x}{2} + \frac{-16}{2}
\][/tex]
[tex]\[
y = -x - 8
\][/tex]
Now, the equation has been converted into slope-intercept form [tex]\(y = mx + b\)[/tex], where the slope [tex]\(m\)[/tex] is [tex]\(-1\)[/tex] and the y-intercept [tex]\(b\)[/tex] is [tex]\(-8\)[/tex].
So, the slope-intercept form of the equation [tex]\(2x + 2y = -16\)[/tex] is:
[tex]\[
y = -x - 8
\][/tex]
