y = 5x - 7 solve for x and determine if it's a function of x

To solve the equation \( y = 5x - 7 \) for \( x \), we need to isolate \( x \) on one side of the equation.

### Step 1: Solve for \( x \)
Starting with the equation:
\[
y = 5x - 7
\]
Add \( 7 \) to both sides to get:
\[
y + 7 = 5x
\]
Next, divide both sides by \( 5 \) to solve for \( x \):
\[
x = \frac{y + 7}{5}
\]

So, the solution for \( x \) is:
\[
x = \frac{y + 7}{5}
\]

### Step 2: Determine if \( y = 5x - 7 \) is a function of \( x \)
A relation is a function if for each input \( x \), there is exactly one output \( y \). The given equation \( y = 5x - 7 \) is a linear equation in the form \( y = mx + b \), where \( m \) and \( b \) are constants. This equation represents a straight line, and for every value of \( x \), there is a unique value of \( y \).

Thus, \( y = 5x - 7 \) is indeed a function of \( x \).

### Summary:
1. The solution for \( x \) is \( x = \frac{y + 7}{5} \).
2. \( y = 5x - 7 \) is a function of \( x \).

Would you like any further details or explanations?

Here are some related questions:
1. How can you determine if any equation represents a function?
2. What are the characteristics of a linear function?
3. How does the slope \( m \) in \( y = mx + b \) affect the graph of the function?
4. Can you solve for \( x \) if the equation was quadratic instead of linear?
5. What happens to the function if the constant term \( -7 \) is changed?

**Tip:** When graphing linear functions, the slope \( m \) determines the steepness, and the y-intercept \( b \) determines where the line crosses the y-axis.

Learn how to solve the equation y = 5x - 7 for x and determine if it represents a function of x. This problem covers linear equations and function definitions. Suitable for students in Grades 8-10.

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