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?

$y=8x-3$

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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

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

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Given the following graph, determine whether function is constant

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!

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