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

What is the solution to the following inequality?

$$ 10x-4\leq-3x-8 $$

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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