Sure! Let's solve the given equation step-by-step to find its slope and y-intercept.
1. Start with the given equation:
[tex]\[
y + 4 = -\frac{5}{2}(x + 3)
\][/tex]
2. Distribute [tex]\(-\frac{5}{2}\)[/tex] to the terms inside the parentheses on the right-hand side:
[tex]\[
y + 4 = -\frac{5}{2} \cdot x + -\frac{5}{2} \cdot 3
\][/tex]
3. Simplify the right-hand side:
[tex]\[
y + 4 = -\frac{5}{2}x - \frac{15}{2}
\][/tex]
4. Isolate [tex]\(y\)[/tex] by subtracting 4 from both sides of the equation:
[tex]\[
y = -\frac{5}{2}x - \frac{15}{2} - 4
\][/tex]
5. Combine the constant terms on the right-hand side. Convert 4 to a fraction with a common denominator:
[tex]\[
y = -\frac{5}{2}x - \frac{15}{2} - \frac{8}{2}
\][/tex]
6. Add the fractions on the right-hand side:
[tex]\[
y = -\frac{5}{2}x - \frac{23}{2}
\][/tex]
So, the equation is now in slope-intercept form [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept.
- The slope [tex]\(m\)[/tex] is: [tex]\(-\frac{5}{2}\)[/tex]
- The y-intercept [tex]\(b\)[/tex] is: [tex]\(-\frac{23}{2}\)[/tex]
To summarize:
- The slope [tex]\(m\)[/tex] is [tex]\(-2.5\)[/tex]
- The y-intercept [tex]\(b\)[/tex] is [tex]\(-11.5\)[/tex]
Thus, the equation in slope-intercept form is:
[tex]\[
y = -2.5x - 11.5
\][/tex]
