Identify the Matching Equation for the Linear Graph

Which of the following equations corresponds to the function represented in the graph?

To solve the problem, follow these steps:

• Step 1: Identify two clear points on the line from the graph.
• Step 2: Determine the slope using these two points.
• Step 3: Find the y-intercept using the slope-intercept form of the equation.
• Step 4: Compare the derived equation to the provided choices.

Now, let's work through each step:

Step 1: Upon examining the graph, let's assume it passes through the points $(0, 4)$ and $(3, 0)$.

Step 2: Calculate the slope $m$ using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$:
$m = \frac{0 - 4}{3 - 0} = \frac{-4}{3}$.

Step 3: Use the y-intercept point, which is already identified as $(0, 4)$. Hence, $b = 4$.

Thus, the equation of the line is $y = -\frac{4}{3}x + 4$.

Step 4: Compare this to the choices: The correct choice is $y = -\frac{4}{3}x + 4$, which matches the equation we derived.

Therefore, the solution to the problem is $y = -\frac{4}{3}x + 4$.