Consider the following relation.

−3y+7x=−3−3y+7x=−3

Step 1 of 2 :  

Determine the domain and range for the relation in interval notation.

Let's analyze the given relation:

\[
-3y + 7x = -3
\]

### Step 1: Simplify the equation for \(y\)

To make it easier to analyze the domain and range, we solve for \(y\) in terms of \(x\).

\[
-3y = -3 - 7x
\]

Now divide both sides by \(-3\):

\[
y = \frac{-3 - 7x}{-3}
\]

Simplify:

\[
y = 1 + \frac{7x}{3}
\]

This is now a linear equation in the form:

\[
y = 1 + \frac{7}{3}x
\]

### Step 2: Determine the domain

For linear equations, \(y\) is defined for all real values of \(x\). There are no restrictions on \(x\), so the **domain** is:

\[
\text{Domain}: (-\infty, \infty)
\]

### Step 3: Determine the range

Since this is a linear equation, \(y\) can also take all real values. Therefore, the **range** is:

\[
\text{Range}: (-\infty, \infty)
\]

### Conclusion:
- **Domain**: \((- \infty, \infty)\)
- **Range**: \((- \infty, \infty)\)

Would you like further explanation or details on any of the steps?

Here are five related questions:
1. What is the slope of the linear equation \(y = 1 + \frac{7}{3}x\)?
2. How do you find the intercepts of a linear equation like this?
3. How do you graph a linear equation?
4. What are the differences between linear and quadratic relations in terms of domain and range?
5. How do you find the inverse of a linear function?

**Tip:** When working with linear equations, remember that the slope tells you how steep the line is, and the intercept shows where it crosses the y-axis.

Consider the following relation: -3y + 7x = -3. Step 1 of 2: Determine the domain and range for the relation in interval notation.

Learn how to determine the domain and range of the linear equation -3y + 7x = -3. This problem provides a step-by-step solution, exploring algebraic concepts of linear equations, and how to express the domain and range in interval notation. Suitable for students in Grades 8-10.

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