Find the Rate of Change: Analyzing y=-4x+3

Linear Equations with Negative Slopes

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

y=4x+3 y=-4x+3

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Step-by-step video solution

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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

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1

Understand the problem

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

y=4x+3 y=-4x+3

2

Step-by-step solution

To solve this problem, we need to determine the rate of change of the linear equation given by:

y=4x+3 y = -4x + 3

The standard form for a linear equation is:

y=mx+b y = mx + b

where m m represents the slope of the line. The slope indicates the rate of change of the function, which describes how much the value of y y changes for a unit change in x x .

In the equation y=4x+3 y = -4x + 3 , the slope m m is 4-4. This means that for every unit increase in x x , the value of y y decreases by 4. Thus, the rate of change for this equation is 4-4.

Therefore, the rate of change is 4 -4 .

3

Final Answer

4 -4

Key Points to Remember

Essential concepts to master this topic
  • Slope-Intercept Form: In y = mx + b, m is always the rate of change
  • Identification Technique: For y = -4x + 3, coefficient of x is -4
  • Verification: Check units change: x increases 1, y decreases 4 ✓

Common Mistakes

Avoid these frequent errors
  • Confusing slope with y-intercept
    Don't identify the constant term 3 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 slope (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

Why is the rate of change negative?

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A negative rate of change means the line is decreasing. As x increases by 1, y decreases by 4. This creates a downward-sloping line from left to right.

What's the difference between slope and rate of change?

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They're the same thing! Both terms describe how much y changes when x increases by 1. In y=4x+3 y = -4x + 3 , the slope and rate of change are both -4.

How do I remember which number is the slope?

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In y=mx+b y = mx + b form, the slope is always the coefficient of x (the number multiplying x). The other number is the y-intercept.

What does the 3 represent in this equation?

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The number 3 is the y-intercept, not the rate of change. It tells us where the line crosses the y-axis when x=0 x = 0 .

Can I check my answer by plugging in values?

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Yes! Pick any x-value, calculate y, then pick x + 1 and see if y decreases by 4. For example: when x = 1, y = -1; when x = 2, y = -5. The difference is -4 ✓

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