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.