Find the Rate of Change: Analyzing y = -6x Linear Function

Q: Why is the rate of change negative in this problem?

The rate of change is negative (-6) because as x increases, y decreases. This means the line slopes downward from left to right - for every 1 unit x increases, y drops by 6 units.

Q: What's the difference between slope and rate of change?

They're the same thing! Rate of change is just another way to say slope. Both tell you how much y changes when x changes by 1 unit.

Q: How do I find rate of change if the equation looks different?

First, rearrange the equation to slope-intercept form $ y = mx + b $. Then the coefficient of x is your rate of change, no matter how the original equation was written!

Q: Can rate of change be a fraction or decimal?

Absolutely! Rate of change can be any real number - positive, negative, whole numbers, fractions, or decimals. In this case, it's the whole number -6.

Slope Identification with Direct Linear Functions

Given the linear function:

$y=-6x$

What is the rate of change of the function?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the rate of change of the function

00:03 The rate of change is the slope of the function (M)

00:07 We will use the line equation

00:10 We will compare and find the slope of the function using the line equation

00:15 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given the linear function:

$y=-6x$

What is the rate of change of the function?

Step-by-step solution

To solve this problem, let's follow these steps:

Step 1: Identify the form of the given function
Step 2: Compare the equation with the standard slope-intercept form
Step 3: Extract the value of the slope from the equation

Now, let's work through each step:

Step 1: The given linear function is $y = -6x$ . This is presented in the form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

Step 2: Comparing $y = -6x$ with $y = mx + b$ , we see that the equation lacks a constant term, indicating $b = 0$ . The slope $m$ is the coefficient of $x$ .

Step 3: The coefficient of $x$ is $-6$ , so the slope $m$ is $-6$ . Thus, the rate of change of the function is $-6$ .

Therefore, the solution to the problem is $m = -6$ .

Final Answer

$m=-6$

Key Points to Remember

Essential concepts to master this topic

Rule: In $y = mx + b$ form, m equals the rate of change
Technique: Coefficient of x in $y = -6x$ gives slope = -6
Check: Verify rate of change: when x increases by 1, y decreases by 6 ✓

Common Mistakes

Avoid these frequent errors

Confusing slope with y-intercept
Don't look for the constant term when finding slope = wrong answer! The y-intercept (b) doesn't affect rate of change. Always identify the coefficient of x as your slope value.

Practice Quiz

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For the function in front of you, the slope is?

FAQ

Everything you need to know about this question

Why is the rate of change negative in this problem?

The rate of change is negative (-6) because as x increases, y decreases. This means the line slopes downward from left to right - for every 1 unit x increases, y drops by 6 units.

What's the difference between slope and rate of change?

They're the same thing! Rate of change is just another way to say slope. Both tell you how much y changes when x changes by 1 unit.

Where is the y-intercept in this equation?

The y-intercept is 0 because there's no constant term. The equation $y = -6x$ means $y = -6x + 0$ , so the line passes through the origin (0,0).

How do I find rate of change if the equation looks different?

First, rearrange the equation to slope-intercept form $y = mx + b$ . Then the coefficient of x is your rate of change, no matter how the original equation was written!

Can rate of change be a fraction or decimal?

Absolutely! Rate of change can be any real number - positive, negative, whole numbers, fractions, or decimals. In this case, it's the whole number -6.

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