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

Given a function that is positive from the beginning of the axes. Plus the point (7,9) on the graph of the function. Find the equation for the function.

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 $y = 1\frac{2}{7}x$.