Find the Rate of Change: Analyzing y=x-4 Linear Function

Slope Identification with Standard Form

Given the linear function:

y=x4 y=x-4

What is the rate of change of the function?

❤️ 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 Find the slope of the function
00:04 We'll use the formula to represent a linear function
00:07 We can see that the coefficient of X (M) is the slope of the function
00:14 We'll find the function's slope using the coefficient of X
00:19 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 linear function:

y=x4 y=x-4

What is the rate of change of the function?

2

Step-by-step solution

The problem asks to find the rate of change of the linear function y=x4 y = x - 4 . This function is in the form of y=mx+b y = mx + b , where:

  • m m is the slope, representing the rate of change of the function.
  • b b is the y-intercept, but it is not relevant for finding the rate of change.

For the function y=x4 y = x - 4 , we can compare it with the standard form y=mx+b y = mx + b to identify:

m=1 m = 1 .

Therefore, the rate of change of the function is determined by the coefficient of x x , which is 1.

Hence, the rate of change of the function is m=1 m = 1 .

The correct answer is: m=1 m = 1 .

3

Final Answer

m=1 m=1

Key Points to Remember

Essential concepts to master this topic
  • Slope-Intercept Form: In y=mx+b y = mx + b , coefficient m is the slope
  • Technique: For y=x4 y = x - 4 , coefficient of x is 1
  • Check: Rate of change = 1 means y increases 1 unit per x unit ✓

Common Mistakes

Avoid these frequent errors
  • Confusing the y-intercept with the slope
    Don't think the rate of change is -4 because it's the most obvious number! The -4 is just the y-intercept where the line crosses the y-axis. Always identify the coefficient of x as the slope, which is 1 in y=x4 y = x - 4 .

Practice Quiz

Test your knowledge with interactive questions

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

XY

FAQ

Everything you need to know about this question

Why is the slope 1 and not -4?

+

In y=mx+b y = mx + b form, the slope is always the coefficient of x. Since y=x4 y = x - 4 can be written as y=1x+(4) y = 1x + (-4) , the slope is 1 and the y-intercept is -4.

What does a slope of 1 actually mean?

+

A slope of 1 means the line rises 1 unit up for every 1 unit right. It's a 45-degree angle going upward from left to right!

How do I find slope when x doesn't have a visible coefficient?

+

When you see just x (like in y=x4 y = x - 4 ), there's an invisible 1 in front of it. So x=1x x = 1x , making the slope equal to 1.

Is the rate of change always the same as the slope?

+

Yes, for linear functions! Rate of change and slope are the same thing - they both measure how much y changes when x increases by 1.

What if the equation isn't in y = mx + b form?

+

You'll need to rearrange it first. Solve for y to get it in slope-intercept form, then identify the coefficient of x as your slope.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Linear 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