Find the Rate of Change in y=5x+4: Linear Equation Analysis

Slope-Intercept Form with Rate Identification

For the following straight line equation, state what is the rate of change?

y=5x+4 y=5x+4

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 What is the rate of change of the function?
00:02 The rate of change of the function is the slope of the function (X coefficient)
00:05 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

For the following straight line equation, state what is the rate of change?

y=5x+4 y=5x+4

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Understand the equation format
  • Step 2: Identify the slope from the equation
  • Step 3: Match the slope to the given choices

Now, let's work through each step:
Step 1: The equation y=5x+4 y = 5x + 4 is in the slope-intercept form y=mx+b y = mx + b , where m m is the slope.
Step 2: From the equation, the slope m m is the coefficient of x x , which is 5. This represents the rate of change for this line.
Step 3: Among the choices, the correct choice representing the rate of change is 5.

Therefore, the solution to the problem is 5 5

3

Final Answer

5

Key Points to Remember

Essential concepts to master this topic
  • Rule: In y=mx+b y = mx + b , m equals the rate of change
  • Technique: Identify coefficient of x: in y=5x+4 y = 5x + 4 , coefficient is 5
  • Check: Rate of change = slope = 5, not y-intercept = 4 ✓

Common Mistakes

Avoid these frequent errors
  • Confusing slope with y-intercept
    Don't choose the constant term (4) as the rate of change = wrong answer! The y-intercept shows where the line crosses the y-axis, not how steep it is. Always identify the coefficient of x as the rate of change.

Practice Quiz

Test your knowledge with interactive questions

Look at the graph below and determine whether the function's rate of change is constant or not:

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111–3–3–3–2–2–2–1–1–1111222333444555000

FAQ

Everything you need to know about this question

What's the difference between slope and y-intercept?

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Slope (rate of change) tells you how steep the line is - it's the coefficient of x. The y-intercept tells you where the line crosses the y-axis - it's the constant term.

Why is the rate of change called the slope?

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Rate of change and slope mean the same thing! Both describe how much y changes when x increases by 1. In y=5x+4 y = 5x + 4 , y increases by 5 for every 1 unit increase in x.

How do I remember which number is which in y = mx + b?

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Use this memory trick: m comes before b in the alphabet, just like the coefficient of x comes before the constant term. Also remember: m = slope, b = y-intercept.

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

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You need to rearrange the equation to get y by itself on one side. Once it's in slope-intercept form, the coefficient of x is your rate of change.

Can the rate of change be negative?

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Yes! A negative rate of change means the line slopes downward from left to right. For example, in y=3x+2 y = -3x + 2 , the rate of change is -3.

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