Find the Rate of Change in y=8x-3: Linear Equation Analysis

Q: What exactly is a rate of change in a linear equation?

The rate of change tells you how much y changes when x increases by 1. In $ y = 8x - 3 $, when x goes up by 1, y goes up by 8!

Q: Why isn't -3 the rate of change?

The number -3 is the y-intercept, not the rate of change. It tells you where the line crosses the y-axis, but it doesn't tell you how steep the line is.

Q: How do I remember which number is the slope?

In $ y = mx + b $ form, m (the coefficient of x) is always the slope. Think: "m for slope, b for y-intercept"!

Q: What if the coefficient of x was negative?

A negative coefficient means the line slopes downward. For example, in $ y = -5x + 2 $, the rate of change is -5, meaning y decreases by 5 when x increases by 1.

Q: Can I verify my answer is 8?

Yes! Pick any two points on the line and calculate: $ \frac{\text{change in y}}{\text{change in x}} $. You'll always get 8 for this equation!

Linear Equations with Slope-Intercept Form

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

$y=8x-3$

❤️ 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 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

Understand the problem

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

$y=8x-3$

Step-by-step solution

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

Step 1: Recognize the standard form of a linear equation.
Step 2: Identify the coefficient of $x$ as the rate of change.

Now, let's work through each step.
Step 1: Recognize that the given equation $y = 8x - 3$ is in the slope-intercept form $y = mx + b$ , where $m$ is the slope.
Step 2: In this equation, the coefficient of $x$ is 8. Therefore, the coefficient $8$ represents the rate of change or the slope of the line.

Thus, the rate of change for the equation $y = 8x - 3$ is $8$ , which corresponds to choice 1.

Final Answer

$8$

Key Points to Remember

Essential concepts to master this topic

Rule: In y = mx + b, m is the rate of change
Technique: Coefficient of x equals slope: y = 8x - 3 has slope 8
Check: Rate of change = 8 means y increases 8 units for every 1 unit increase in x ✓

Common Mistakes

Avoid these frequent errors

Confusing the y-intercept with the rate of change
Don't identify -3 as the rate of change = wrong slope! The constant term -3 is the y-intercept (where the line crosses the y-axis), not the rate of change. Always remember the coefficient of x (which is 8) represents the rate of change or slope.

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

What exactly is a rate of change in a linear equation?

The rate of change tells you how much y changes when x increases by 1. In $y = 8x - 3$ , when x goes up by 1, y goes up by 8!

Why isn't -3 the rate of change?

The number -3 is the y-intercept, not the rate of change. It tells you where the line crosses the y-axis, but it doesn't tell you how steep the line is.

How do I remember which number is the slope?

In $y = mx + b$ form, m (the coefficient of x) is always the slope. Think: "m for slope, b for y-intercept"!

What if the coefficient of x was negative?

A negative coefficient means the line slopes downward. For example, in $y = -5x + 2$ , the rate of change is -5, meaning y decreases by 5 when x increases by 1.

Can I verify my answer is 8?

Yes! Pick any two points on the line and calculate: $\frac{\text{change in y}}{\text{change in x}}$ . You'll always get 8 for this equation!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 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