Find the Rate of Change: Solving -x+y=0 Linear Equation

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

Rate of change is the slope of the line! It tells you how much y increases (or decreases) for every 1-unit increase in x. Think of it like the steepness of a hill.

Q: Why do I need to convert to y = mx + b form?

The slope-intercept form $ y = mx + b $ makes it super easy to identify the slope (m). The coefficient in front of x is always your rate of change!

Q: How do I move -x to the other side correctly?

Add x to both sides of the equation. So $ -x + y = 0 $ becomes $ y = x $. Remember: what you do to one side, you must do to the other!

Q: What if the coefficient of x is missing?

If you see just x (like in $ y = x $), the coefficient is 1! It's invisible but it's there. So the slope is 1, not 0.

Q: Can the rate of change be negative?

Absolutely! If you get something like $ y = -2x + 3 $, the rate of change is -2. This means y decreases by 2 units for every 1-unit increase in x.

Linear Equations with Standard Form Conversion

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

$-x+y=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's find the slope of the graph.

00:10 First, we'll arrange the equation like a linear equation.

00:14 To do this, we need to isolate Y.

00:18 Remember, every number is actually multiplied by 1.

00:22 Look at the coefficient of X. That's our slope, showing the rate of change.

00:28 And that's how we solve this problem!

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?

$-x+y=0$

Step-by-step solution

To solve this problem, we need to determine the rate of change of the given line equation $-x + y = 0$ .

Let's proceed step-by-step:

Step 1: Identify the given equation, which is $-x + y = 0$ .
Step 2: Rearrange the equation to fit the slope-intercept form $y = mx + b$ .
To do this, add $x$ to both sides:
$y = x$
Step 3: Identify the slope $m$ .
In the equation $y = x$ , the term $x$ has a coefficient of $1$ , which means the slope $m = 1$ .
Step 4: Interpret the result.
The slope $1$ is the rate of change of the line, meaning for every unit increase in $x$ , $y$ increases by 1 unit.

Therefore, the rate of change of the line is $1$ .

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Rate of Change: The slope represents how y changes per unit increase in x
Technique: Convert $-x + y = 0$ to slope-intercept form $y = x$
Check: Coefficient of x gives slope: $y = 1x$ means slope = 1 ✓

Common Mistakes

Avoid these frequent errors

Confusing coefficient signs when rearranging
Don't keep the negative sign with x when moving it = wrong slope! Students often write y = -x instead of y = x, giving slope -1 instead of 1. Always carefully track positive and negative signs when moving terms across the equals sign.

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 rate of change in a linear equation?

Rate of change is the slope of the line! It tells you how much y increases (or decreases) for every 1-unit increase in x. Think of it like the steepness of a hill.

Why do I need to convert to y = mx + b form?

The slope-intercept form $y = mx + b$ makes it super easy to identify the slope (m). The coefficient in front of x is always your rate of change!

How do I move -x to the other side correctly?

Add x to both sides of the equation. So $-x + y = 0$ becomes $y = x$ . Remember: what you do to one side, you must do to the other!

What if the coefficient of x is missing?

If you see just x (like in $y = x$ ), the coefficient is 1! It's invisible but it's there. So the slope is 1, not 0.

Can the rate of change be negative?

Absolutely! If you get something like $y = -2x + 3$ , the rate of change is -2. This means y decreases by 2 units for every 1-unit increase in x.

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