Question
what is the initial value and rate of change if the points (0,0) and (2,3) which is in quadrant 1
Answers
GPT-4o mini
To find the initial value and the rate of change between the points (0, 0) and (2, 3), we can consider these points in the context of a linear relationship.
1. **Initial Value**: This is the value of the function when \( x = 0 \). From the point (0, 0), we see that when \( x = 0 \), \( y = 0 \). Therefore, the initial value is 0.
2. **Rate of Change (Slope)**: The rate of change can be calculated using the formula for the slope of a line, which is given by:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
For the points \( (0, 0) \) and \( (2, 3) \):
- \( (x_1, y_1) = (0, 0) \)
- \( (x_2, y_2) = (2, 3) \)
Plugging in the values:
\[
\text{slope} = \frac{3 - 0}{2 - 0} = \frac{3}{2}
\]
So, the initial value is **0**, and the rate of change (slope) is **\(\frac{3}{2}\)**.
1. **Initial Value**: This is the value of the function when \( x = 0 \). From the point (0, 0), we see that when \( x = 0 \), \( y = 0 \). Therefore, the initial value is 0.
2. **Rate of Change (Slope)**: The rate of change can be calculated using the formula for the slope of a line, which is given by:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
For the points \( (0, 0) \) and \( (2, 3) \):
- \( (x_1, y_1) = (0, 0) \)
- \( (x_2, y_2) = (2, 3) \)
Plugging in the values:
\[
\text{slope} = \frac{3 - 0}{2 - 0} = \frac{3}{2}
\]
So, the initial value is **0**, and the rate of change (slope) is **\(\frac{3}{2}\)**.