Find the Rate of Change: Analyzing y=-3/8-4x Linear Equation

Q: Why is the rate of change -4 and not positive 4?

The sign matters! A negative rate of change means the line is decreasing - as x increases, y decreases. The coefficient of x includes its sign, so the rate of change is exactly -4.

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

They're the same thing! Rate of change is just another name for slope. Both tell you how much y changes when x increases by 1 unit.

Q: How do I know which number is the slope in any linear equation?

In $ y = mx + b $ form, the slope is always the coefficient of x. Look for the number (including its sign) that's multiplied by x.

Q: What does -3/8 represent in this equation?

The $ -\frac{3}{8} $ is the y-intercept - where the line crosses the y-axis. It's the constant term, not the rate of change.

Q: Can I rewrite this equation to make it clearer?

Yes! You can rewrite $ y = -\frac{3}{8} - 4x $ as $ y = -4x - \frac{3}{8} $ to match the standard mx + b format more clearly.

Linear Equations with Negative Coefficients

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

$y=-\frac{3}{8}-4x$

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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?

00:03 We want to arrange the equation that represents a line

00:06 The rate of change of the function is the slope of the function (X coefficient)

00:10 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

$y=-\frac{3}{8}-4x$

Step-by-step solution

To determine the rate of change for the given line equation, we recognize that the equation $y = -\frac{3}{8} - 4x$ is in the slope-intercept form $y = mx + b$ , where $m$ is the slope and represents the rate of change.

In the equation provided, the term $-4x$ indicates that the slope or rate of change is $m = -4$ .

Thus, the rate of change of the given straight line is $-4$ .

Comparing this to the provided choices, the correct answer is:

Choice id "2": $-4$

Therefore, the rate of change for the linear equation is $-4$ .

Final Answer

$-4$

Key Points to Remember

Essential concepts to master this topic

Slope-Intercept Form: In $y = mx + b$ , m is the rate of change
Technique: Identify coefficient of x: in $y = -\frac{3}{8} - 4x$ , slope is -4
Check: Rate of change equals slope = coefficient of x term ✓

Common Mistakes

Avoid these frequent errors

Confusing y-intercept with slope
Don't identify $-\frac{3}{8}$ as the rate of change = wrong answer! This is the y-intercept (constant term), not the slope. Always look for the coefficient of the x term to find 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:

FAQ

Everything you need to know about this question

Why is the rate of change -4 and not positive 4?

The sign matters! A negative rate of change means the line is decreasing - as x increases, y decreases. The coefficient of x includes its sign, so the rate of change is exactly -4.

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

They're the same thing! Rate of change is just another name for slope. Both tell you how much y changes when x increases by 1 unit.

How do I know which number is the slope in any linear equation?

In $y = mx + b$ form, the slope is always the coefficient of x. Look for the number (including its sign) that's multiplied by x.

What does -3/8 represent in this equation?

The $-\frac{3}{8}$ is the y-intercept - where the line crosses the y-axis. It's the constant term, not the rate of change.

Can I rewrite this equation to make it clearer?

Yes! You can rewrite $y = -\frac{3}{8} - 4x$ as $y = -4x - \frac{3}{8}$ to match the standard mx + b format more clearly.

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