Question

which has the larger y intercept and the greatest rate of change

-1,-1
0,3
1,7
2,11
4,19
5,23

0,2
1,3
2,5
3,9
4,17

anonymous

Answer 1

To determine which dataset has the larger y-intercept and the greatest rate of change, let's first define the two sets of points given:

**Dataset 1:**
- (-1, -1)
- (0, 3)
- (1, 7)
- (2, 11)
- (4, 19)
- (5, 23)

**Dataset 2:**
- (0, 2)
- (1, 3)
- (2, 5)
- (3, 9)
- (4, 17)

### 1. Finding the y-intercepts

The y-intercept is the value of y when x = 0.

- **Dataset 1 (x = 0)**: y = 3
- **Dataset 2 (x = 0)**: y = 2

**Conclusion**: Dataset 1 has the larger y-intercept (3 vs. 2).

### 2. Calculating the rate of change (slope)

The rate of change (or slope) can be calculated using the formula:

\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]

We will calculate the slope between the first and last points in each dataset to assess the overall rate of change:

#### **Dataset 1:**
Using the points (0, 3) and (5, 23):

\[
\text{slope} = \frac{23 - 3}{5 - 0} = \frac{20}{5} = 4
\]

#### **Dataset 2:**
Using the points (0, 2) and (4, 17):

\[
\text{slope} = \frac{17 - 2}{4 - 0} = \frac{15}{4} = 3.75
\]

### **Final Summary:**

- **Larger y-intercept**: Dataset 1 (3 vs. 2)
- **Greatest rate of change**: Dataset 1 (4 vs. 3.75)

**Dataset 1 has both the larger y-intercept and the greatest rate of change.**