Classify the Linear Function: Understanding y=2-3x

Q: How do I know if a linear function is increasing or decreasing?

Look at the slope (coefficient of x)! If it's positive, the function increases. If it's negative, the function decreases. In $ y = 2 - 3x $, the slope is -3, so it's decreasing.

Q: Why does the order of terms matter?

The order doesn't change the slope! Whether you write $ y = 2 - 3x $ or $ y = -3x + 2 $, the slope is still -3. Always focus on the coefficient of x to determine the function's behavior.

Q: What does it mean for a function to be decreasing?

A decreasing function means as x gets larger, y gets smaller. Think of it like going downhill - as you move right on the graph, you go down!

Q: Can I test this with actual numbers?

Absolutely! Try x = 0: $ y = 2 - 3(0) = 2 $. Try x = 1: $ y = 2 - 3(1) = -1 $. See how y went from 2 to -1? That's decreasing!

Q: What if the slope was zero?

If the slope equals zero, like $ y = 2 - 0x = 2 $, then the function is constant. The y-value never changes no matter what x equals.

Linear Functions with Negative Slopes

Which best describes the function below?

$y=2-3x$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's find out if the function goes up, goes down, or stays the same.

00:10 We start by using the equation of a straight line.

00:14 Next, let's rearrange the equation so it looks like a straight line equation.

00:19 Here, the coefficient of X gives us the slope of the graph.

00:26 The slope is negative, so the function is going down.

00:31 And that's how we solve this problem!

Step-by-step written solution

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Understand the problem

Which best describes the function below?

$y=2-3x$

Step-by-step solution

To determine the characteristic of the function $y = 2 - 3x$ , we will evaluate the slope:

The given function is in the form $y = mx + b$ , which indicates a linear equation. Here, $y = 2 - 3x$ can be rearranged as $y = -3x + 2$ , showing that $m = -3$ .
The slope $m$ is $-3$ .
In a linear function, the sign of the slope $m$ determines the function's behavior:

If the slope $m$ is positive ( $m > 0$ ), the function is increasing.
If the slope $m$ is negative ( $m < 0$ ), the function is decreasing.
If the slope $m = 0$ , the function is constant.

Since $m = -3$ , which is negative, we conclude that the function is decreasing.

Therefore, the function described by $y = 2 - 3x$ is decreasing.

Final Answer

The function is decreasing.

Key Points to Remember

Essential concepts to master this topic

Slope Rule: Negative slope means function decreases as x increases
Standard Form: Rewrite $y = 2 - 3x$ as $y = -3x + 2$
Check: Pick two x-values: when x increases, y decreases ✓

Common Mistakes

Avoid these frequent errors

Confusing coefficient order with slope sign
Don't think $y = 2 - 3x$ has positive slope because 2 comes first = wrong classification! The coefficient of x determines behavior, not the constant term. Always identify the slope by looking at the x coefficient: -3 means decreasing.

Practice Quiz

Test your knowledge with interactive questions

Look at the linear function represented in the diagram.

When is the function positive?

FAQ

Everything you need to know about this question

How do I know if a linear function is increasing or decreasing?

Look at the slope (coefficient of x)! If it's positive, the function increases. If it's negative, the function decreases. In $y = 2 - 3x$ , the slope is -3, so it's decreasing.

Why does the order of terms matter?

The order doesn't change the slope! Whether you write $y = 2 - 3x$ or $y = -3x + 2$ , the slope is still -3. Always focus on the coefficient of x to determine the function's behavior.

What does it mean for a function to be decreasing?

A decreasing function means as x gets larger, y gets smaller. Think of it like going downhill - as you move right on the graph, you go down!

Can I test this with actual numbers?

Absolutely! Try x = 0: $y = 2 - 3(0) = 2$ . Try x = 1: $y = 2 - 3(1) = -1$ . See how y went from 2 to -1? That's decreasing!

What if the slope was zero?

If the slope equals zero, like $y = 2 - 0x = 2$ , then the function is constant. The y-value never changes no matter what x equals.

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Classify the Linear Function: Understanding y=2-3x

Linear Functions with Negative Slopes

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How do I know if a linear function is increasing or decreasing?

Why does the order of terms matter?

What does it mean for a function to be decreasing?

Can I test this with actual numbers?

What if the slope was zero?

🌟 Unlock Your Math Potential

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