Find the Rate of Change in the Linear Equation: -5x+y=3

Q: Why isn't the rate of change -5 since that's the coefficient of x?

The coefficient in standard form isn't always the slope! When you have $ -5x + y = 3 $, you need to solve for y first. This gives $ y = 5x + 3 $, so the rate of change is positive 5.

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

They're the same thing! Rate of change describes how much y changes when x increases by 1 unit. In linear equations, this is exactly what slope measures.

Q: How do I remember to rearrange the equation first?

Think of it as "get y by itself". The slope-intercept form $ y = mx + b $ makes the slope obvious - it's the number multiplying x!

Q: Can the rate of change be negative?

Absolutely! If your final equation is $ y = -3x + 7 $, then the rate of change is -3. This means y decreases by 3 units for every 1 unit increase in x.

Q: What if there's no x term in my final equation?

If you get something like $ y = 4 $, that's a horizontal line with rate of change = 0. The y-value stays constant no matter how x changes.

Rate of Change with Standard Form Equations

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

$-5x+y=3$

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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 to represent a straight line, so we'll isolate Y

00:09 The rate of change of the function is the slope of the function

00:12 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?

$-5x+y=3$

Step-by-step solution

To solve this problem, let's follow these steps:

Step 1: Convert the given equation to the slope-intercept form.
Step 2: Identify the slope as the rate of change.

Now, let's work through each step:

Step 1: Convert to Slope-Intercept Form
The given equation is $-5x + y = 3$ . To convert it to the slope-intercept form, solve for $y$ :

Add $5x$ to both sides to isolate $y$ :

$y = 5x + 3$

Here, the equation is now in the form $y = mx + b$ , where $m$ represents the slope.

Step 2: Identify the Slope
From the equation $y = 5x + 3$ , we can see that the slope $m$ is $5$ .

Therefore, the rate of change for the given line equation is $5$ .

Final Answer

$5$

Key Points to Remember

Essential concepts to master this topic

Rule: Rate of change equals the coefficient of x after rearranging
Technique: Convert -5x + y = 3 to y = 5x + 3
Check: Slope m = 5 means y increases 5 units per x unit ✓

Common Mistakes

Avoid these frequent errors

Using the coefficient of x from standard form directly
Don't use -5 as the rate of change from -5x + y = 3! This ignores the negative sign's effect when solving for y. Always rearrange to slope-intercept form y = mx + b first, then identify m as 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 isn't the rate of change -5 since that's the coefficient of x?

The coefficient in standard form isn't always the slope! When you have $-5x + y = 3$ , you need to solve for y first. This gives $y = 5x + 3$ , so the rate of change is positive 5.

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

They're the same thing! Rate of change describes how much y changes when x increases by 1 unit. In linear equations, this is exactly what slope measures.

How do I remember to rearrange the equation first?

Think of it as "get y by itself". The slope-intercept form $y = mx + b$ makes the slope obvious - it's the number multiplying x!

Can the rate of change be negative?

Absolutely! If your final equation is $y = -3x + 7$ , then the rate of change is -3. This means y decreases by 3 units for every 1 unit increase in x.

What if there's no x term in my final equation?

If you get something like $y = 4$ , that's a horizontal line with rate of change = 0. The y-value stays constant no matter how x changes.

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