Find the Rate of Change: Analyzing y = -2x + 1

Given the linear function:

$y=-2x+1$

What is the rate of change of the function?

Video Solution

Solution Steps

00:06 Let's find how fast the function changes.

00:09 The rate of change is like the slope. It's how steep the function is.

00:15 We'll use the equation for a straight line to help us.

00:19 Let's compare and determine the slope of the function using this equation.

00:24 And that's how we solve this problem. Nice work!

Step-by-Step Solution

To determine the rate of change of the function given by the equation $y = -2x + 1$ , we will follow these steps:

Step 1: Recognize that the equation is written in slope-intercept form, $y = mx + b$ , where $m$ is the slope, or rate of change.
Step 2: Identify the coefficient of $x$ in the given equation. Here, the equation $y = -2x + 1$ reveals that the coefficient of $x$ is $-2$ .

This coefficient $-2$ directly represents the slope $m$ of the function.

Therefore, the rate of change of the function is $m = -2$ .