# What is the rate of change of y=-x+2?

Mar 9, 2018

$- 1$

#### Explanation:

Rate of change of means we have to calculate the slope of the line. This is the same as calculating the derivative of the function:

$\implies \frac{d}{\mathrm{dx}} - x + 2$

$\implies \frac{d}{\mathrm{dx}} - 1 x + 2$

$\implies \left(\frac{d}{\mathrm{dx}} - 1\right) + \left(\frac{d}{\mathrm{dx}} 2\right)$

The derivative of any constant is always $0$:

$\implies \frac{d}{\mathrm{dx}} - 1 x$

$\implies \frac{d}{\mathrm{dx}} - 1 {x}^{1}$

The power rule states that:

$\frac{d}{\mathrm{dx}} {x}^{n} = n {x}^{n - 1}$

Here, we can substitute:

$\frac{d}{\mathrm{dx}} - 1 {x}^{1}$

becomes:

$\left(- 1 \cdot 1\right) {x}^{1 - 1}$

$= - 1 {x}^{0}$

$= - 1 \cdot 1$

$= - 1$

And there we have our answer.