Calculate Rate of Change: Finding the Slope of y=7-3x

Linear Functions with Negative Slopes

Given the linear function:

y=73x y=7-3x

What is the rate of change of the function?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the rate of change of the function
00:03 Let's arrange the equation
00:06 The rate of change is the slope of the function (M)
00:09 Let's use the straight line equation
00:13 Let's compare and find the function's slope using the straight line equation
00:21 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Given the linear function:

y=73x y=7-3x

What is the rate of change of the function?

2

Step-by-step solution

To identify the rate of change of the linear function y=73x y = 7 - 3x , we need to determine the slope of the equation.

The given function is in the form of y=mx+b y = mx + b , where m m is the slope or rate of change.

In the equation y=73x y = 7 - 3x , we notice that it can be rewritten as y=3x+7 y = -3x + 7 . Comparing this with the standard form y=mx+b y = mx + b , we find that the coefficient of x x is -3, meaning m=3 m = -3 .

Therefore, the rate of change of this linear function is 3-3.

Thus, the correct answer is m=3 m = -3 .

3

Final Answer

m=3 m=-3

Key Points to Remember

Essential concepts to master this topic
  • Standard Form: In y = mx + b, m is the slope
  • Technique: Rewrite y = 7 - 3x as y = -3x + 7
  • Check: Coefficient of x equals slope: -3x means m = -3 ✓

Common Mistakes

Avoid these frequent errors
  • Confusing the y-intercept with the slope
    Don't identify 7 as the slope because it comes first = wrong answer! The 7 is the y-intercept (where the line crosses the y-axis). Always identify the coefficient of x as the slope.

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 negative in this problem?

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The slope is -3 because of the negative sign in front of the 3x term. A negative slope means the line goes downward from left to right - as x increases, y decreases.

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

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In y=mx+b y = mx + b , the slope (m) tells you how steep the line is, while the y-intercept (b) tells you where the line crosses the y-axis. Here, slope = -3 and y-intercept = 7.

Does the order of terms matter?

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No! Whether you write y=73x y = 7 - 3x or y=3x+7 y = -3x + 7 , it's the same equation. The slope is still the coefficient of x, which is -3.

How do I remember which number is the slope?

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Look for the number attached to x! In any linear equation, the coefficient of x is always the slope. If there's no visible number, like in y = x + 2, the coefficient is 1.

What does a slope of -3 mean in real life?

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A slope of -3 means for every 1 unit you move right, you go down 3 units. It's like going down a steep hill - the rate of change is 3 units down per 1 unit across.

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