Analyze the Linear Function: Is y = 3x - 1 Increasing?

Linear Functions with Slope Analysis

Given the following function:

y=3x1 y=3x-1

Is the function increasing or decreasing?

111–1–1–1000

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Is the function increasing or decreasing?
00:04 The function equation according to the given data
00:09 The function's slope is positive according to the given data
00:12 When the function's slope is positive, the function is increasing
00:18 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the following function:

y=3x1 y=3x-1

Is the function increasing or decreasing?

111–1–1–1000

2

Step-by-step solution

To determine whether the function y=3x1 y = 3x - 1 is increasing or decreasing, we need to examine its slope. The function is in the form y=mx+b y = mx + b , where m m is the slope.

For the given function, the slope m=3 m = 3 .

  • If m>0 m > 0 , the function is increasing.
  • If m<0 m < 0 , the function is decreasing.
  • If m=0 m = 0 , the function is constant (neither increasing nor decreasing).

Since the slope m=3 m = 3 is positive, the function is increasing.

Therefore, the function y=3x1 y = 3x - 1 is increasing.

3

Final Answer

Increasing

Key Points to Remember

Essential concepts to master this topic
  • Rule: A positive slope means the function is increasing
  • Technique: Identify slope coefficient: in y=3x1 y = 3x - 1 , slope = 3
  • Check: Pick two x-values: when x increases, y increases ✓

Common Mistakes

Avoid these frequent errors
  • Confusing slope sign with y-intercept
    Don't look at the y-intercept (-1) to determine if function increases = wrong conclusion! The negative y-intercept doesn't affect whether the function increases or decreases. Always examine the slope coefficient (the number with x) to determine the function's behavior.

Practice Quiz

Test your knowledge with interactive questions

Is the function in the graph decreasing? yx

FAQ

Everything you need to know about this question

Why does a positive slope mean the function is increasing?

+

A positive slope means that as x gets larger, y also gets larger! Think of it like climbing uphill - you're moving up as you go forward.

What if the slope were negative instead?

+

If the slope were negative (like -3), then the function would be decreasing. As x increases, y would decrease, like going downhill.

Does the y-intercept affect whether a function increases or decreases?

+

No! The y-intercept only tells you where the line crosses the y-axis. Only the slope determines if the function increases, decreases, or stays constant.

How can I verify this without looking at the graph?

+

Pick any two x-values and calculate their y-values. For example: when x = 0, y=3(0)1=1 y = 3(0) - 1 = -1 . When x = 1, y=3(1)1=2 y = 3(1) - 1 = 2 . Since y increased from -1 to 2, the function is increasing!

What does slope = 3 actually mean?

+

Slope = 3 means for every 1 unit you move right (increase x by 1), you move up 3 units (y increases by 3). This constant upward movement is what makes the function increasing.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Functions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations