To change the equation of a line from standard form, which is [tex]\(3x + 2y = -9\)[/tex], into the slope-intercept form, which is [tex]\(y = mx + b\)[/tex], follow these steps:
1. Isolate [tex]\(y\)[/tex]: Start with the given equation and move the [tex]\(3x\)[/tex] term to the other side by subtracting [tex]\(3x\)[/tex] from both sides. This gives:
[tex]\[
2y = -3x - 9
\][/tex]
2. Solve for [tex]\(y\)[/tex]: To get [tex]\(y\)[/tex] by itself, divide every term in the equation by 2. This will give:
[tex]\[
y = \frac{-3x - 9}{2}
\][/tex]
Simplifying that, you get:
[tex]\[
y = -\frac{3}{2}x - \frac{9}{2}
\][/tex]
Now the equation is in slope-intercept form [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept.
- Slope (m): The coefficient of [tex]\(x\)[/tex] is [tex]\(-\frac{3}{2}\)[/tex], which simplifies to [tex]\(-1.5\)[/tex].
- Y-intercept (b): The constant term is [tex]\(-\frac{9}{2}\)[/tex], which simplifies to [tex]\(-4.5\)[/tex].
So the equation in slope-intercept form is:
[tex]\[
y = -1.5x - 4.5
\][/tex]
Thus, the slope is [tex]\(-1.5\)[/tex] and the y-intercept is [tex]\(-4.5\)[/tex].
