Question

derive 0, -2 and 1,3

Answer 1

It seems like you're asking for the derivation of a function based on the points (0, -2) and (1, 3). However, to clarify, a derivation usually refers to the process of finding the derivative of a function. If you're looking for the equation of a line passing through these points, we can find that.

### Finding the Equation of the Line

1. **Identify the points**:
\[
A = (0, -2) \quad B = (1, 3)
\]

2. **Calculate the slope (m)** of the line using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the coordinates:
\[
m = \frac{3 - (-2)}{1 - 0} = \frac{3 + 2}{1} = \frac{5}{1} = 5
\]

3. **Use the point-slope form of the line equation**:
\[
y - y_1 = m(x - x_1)
\]
Using point A (0, -2):
\[
y - (-2) = 5(x - 0)
\]
Simplifying this:
\[
y + 2 = 5x \implies y = 5x - 2
\]

### Derivative of the Function

Now, if you want to find the derivative of the linear function \( y = 5x - 2 \):

\[
\frac{dy}{dx} = 5
\]

This means that the slope of the line (the rate of change) is constant and equal to 5 at all points along the line.

### Summary

- The equation of the line passing through the points (0, -2) and (1, 3) is:
\[
y = 5x - 2
\]

- The derivative of this function is:
\[
\frac{dy}{dx} = 5
\]

If you meant something else or need further clarification, please let me know!