To find the slope and the [tex]\(y\)[/tex]-intercept for the equation [tex]\(9x + 4y = 20\)[/tex], we need to rewrite the equation in the slope-intercept form, which is [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] represents the slope and [tex]\(b\)[/tex] represents the [tex]\(y\)[/tex]-intercept.
Here are the steps to rearrange the equation into the slope-intercept form:
1. Start with the given equation:
[tex]\[ 9x + 4y = 20 \][/tex]
2. Isolate [tex]\(y\)[/tex] on one side of the equation. To do this, subtract [tex]\(9x\)[/tex] from both sides:
[tex]\[ 4y = -9x + 20 \][/tex]
3. Next, divide every term by 4 to solve for [tex]\(y\)[/tex]:
[tex]\[ y = \frac{-9}{4}x + \frac{20}{4} \][/tex]
4. Simplify the fraction [tex]\(\frac{20}{4}\)[/tex]:
[tex]\[ y = \frac{-9}{4}x + 5 \][/tex]
Now the equation is in slope-intercept form [tex]\(y = mx + b\)[/tex], where:
- The slope [tex]\(m\)[/tex] is [tex]\(\frac{-9}{4} = -2.25\)[/tex]
- The [tex]\(y\)[/tex]-intercept [tex]\(b\)[/tex] is 5.
Therefore, the slope [tex]\(m\)[/tex] is [tex]\(-2.25\)[/tex] and the [tex]\(y\)[/tex]-intercept is [tex]\(5\)[/tex].
