Question

Find the slope and y-intercept for the two linear functions.

A 2-column table with 5 rows. Column 1 is labeled x with entries negative 6, negative 4, 2, 5, 9. Column 2 is labeled y with entries negative 2.5, negative 3, negative 4.5, negative 5.25, and negative 6.25. y = three-halves x + 1.

Identify the slope of the line given in the table:
Identify the y-intercept of the line given in the table:
Identify the slope of the line given by the equation:
Identify the y-intercept of the line given by the equation:

Answer 1

To find the slope and y-intercept for the two linear functions given, we’ll analyze each part separately.

### For the Table:

1. **Data from the table:**
- **x:** -6, -4, 2, 5, 9
- **y:** -2.5, -3, -4.5, -5.25, -6.25

2. **Calculating the slope (m):**
- The slope can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
- We can choose two points from the table to calculate the slope. Let's take the points (-6, -2.5) and (9, -6.25):
- \(y_1 = -2.5, y_2 = -6.25\)
- \(x_1 = -6, x_2 = 9\)
\[
m = \frac{-6.25 - (-2.5)}{9 - (-6)} = \frac{-6.25 + 2.5}{9 + 6} = \frac{-3.75}{15} = -0.25
\]

3. **Identify the slope of the line given in the table:**
- **Slope:** -0.25

4. **Finding the y-intercept (b):**
- To find the y-intercept, we can use the slope-intercept form \(y = mx + b\). We can substitute one point (e.g., (-6, -2.5)) and solve for b:
\[
-2.5 = -0.25(-6) + b
\]
\[
-2.5 = 1.5 + b \implies b = -2.5 - 1.5 = -4
\]

5. **Identify the y-intercept of the line given in the table:**
- **Y-intercept:** -4

### For the Equation \(y = \frac{3}{2}x + 1\):

1. **Identify the slope:**
- The slope (m) is the coefficient of \(x\).
- **Slope:** \(\frac{3}{2}\)

2. **Identify the y-intercept:**
- The y-intercept (b) is the constant term.
- **Y-intercept:** 1

### Summary:

- **Slope of the line given in the table:** -0.25
- **Y-intercept of the line given in the table:** -4
- **Slope of the line given by the equation:** \(\frac{3}{2}\)
- **Y-intercept of the line given by the equation:** 1