Question

Find the slope, y-intercept, and x-intercept for each equation.

y - 4 = 5(x + 2)



8x - 7y = 17

Answer 1

Let's analyze each equation separately to find the slope, y-intercept, and x-intercept.

### 1. For the equation \( y - 4 = 5(x + 2) \):

First, we can rewrite it in slope-intercept form (\( y = mx + b \)), where \( m \) is the slope and \( b \) is the y-intercept.

#### Step 1: Distribute and simplify

\[
y - 4 = 5x + 10
\]
\[
y = 5x + 10 + 4
\]
\[
y = 5x + 14
\]

#### Step 2: Identify the slope and y-intercept

- **Slope (m)**: 5
- **Y-intercept (b)**: 14 (point: (0, 14))

#### Step 3: Find the x-intercept

To find the x-intercept, set \( y = 0 \):

\[
0 = 5x + 14
\]
\[
5x = -14
\]
\[
x = -\frac{14}{5}
\]

So, the x-intercept is \(-\frac{14}{5}\) (point: \(-\frac{14}{5}, 0\)).

### Summary for \( y - 4 = 5(x + 2) \):
- Slope: 5
- Y-intercept: (0, 14)
- X-intercept: \(-\frac{14}{5}, 0\)

---

### 2. For the equation \( 8x - 7y = 17 \):

We'll also rewrite this in slope-intercept form.

#### Step 1: Solve for y

\[
-7y = -8x + 17
\]
\[
y = \frac{8}{7}x - \frac{17}{7}
\]

#### Step 2: Identify the slope and y-intercept

- **Slope (m)**: \( \frac{8}{7} \)
- **Y-intercept (b)**: \( -\frac{17}{7} \) (point: (0, -\frac{17}{7}))

#### Step 3: Find the x-intercept

To find the x-intercept, set \( y = 0 \):

\[
0 = \frac{8}{7}x - \frac{17}{7}
\]
\[
\frac{8}{7}x = \frac{17}{7}
\]
\[
x = \frac{17}{8}
\]

So, the x-intercept is \( \frac{17}{8} \) (point: \( \frac{17}{8}, 0 \)).

### Summary for \( 8x - 7y = 17 \):
- Slope: \( \frac{8}{7} \)
- Y-intercept: (0, \(-\frac{17}{7}\))
- X-intercept: \( \left(\frac{17}{8}, 0\right) \)

---

### Final Summary:
1. **For** \( y - 4 = 5(x + 2) \):
- Slope: 5
- Y-intercept: (0, 14)
- X-intercept: \(-\frac{14}{5}, 0\)

2. **For** \( 8x - 7y = 17 \):
- Slope: \( \frac{8}{7} \)
- Y-intercept: (0, \(-\frac{17}{7}\))
- X-intercept: \( \left(\frac{17}{8}, 0\right) \)