Question

Put in slope intercept form and state the slope and y-intercept.
Y - 8 = 5/2 (x+7)

Answer 1

To convert the equation \( Y - 8 = \frac{5}{2}(x + 7) \) to slope-intercept form, follow these steps:

1. Distribute the \(\frac{5}{2}\) on the right side of the equation:
\[
Y - 8 = \frac{5}{2}x + \frac{5}{2} \cdot 7
\]
\[
Y - 8 = \frac{5}{2}x + \frac{35}{2}
\]

2. Next, add \(8\) to both sides of the equation to isolate \(Y\):
\[
Y = \frac{5}{2}x + \frac{35}{2} + 8
\]

3. Express \(8\) as a fraction with a denominator of \(2\):
\[
8 = \frac{16}{2}
\]
So,
\[
Y = \frac{5}{2}x + \frac{35}{2} + \frac{16}{2}
\]

4. Combine the constant terms on the right side:
\[
Y = \frac{5}{2}x + \frac{35 + 16}{2}
\]
\[
Y = \frac{5}{2}x + \frac{51}{2}
\]

Now, the equation is in slope-intercept form, \( Y = mx + b \), where \(m\) is the slope and \(b\) is the y-intercept.

- The slope \(m\) is \(\frac{5}{2}\).
- The y-intercept \(b\) is \(\frac{51}{2}\).

Thus, the final answer is:

**Slope:** \(\frac{5}{2}\)
**Y-intercept:** \(\frac{51}{2}\) or \(25.5\) when expressed as a decimal.