Find the Function Equation Passing Through Point (7,9): Positive Function Analysis

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information

• Step 2: Calculate the slope of the line passing through the origin and the point (7, 9)

• Step 3: Write the equation of the line that represents the function

Now, let's work through each step:
Step 1: We have the point (7, 9) and know the function is positive starting from the origin, suggesting a line through the origin.

Step 2: Calculate the slope $m$:
Using the points (0, 0) and (7, 9), apply the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$:

$\quad m = \frac{9 - 0}{7 - 0} = \frac{9}{7}$

Step 3: Write the equation of the line:
Since the line passes through the origin, the form is $y = mx$, so:

$\quad y = \frac{9}{7}x$

Therefore, the function equation is $y = 1\frac{2}{7}x$.