Identify the Linear Equation: Match the Graph's Function

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

• Identify two clear points on the graph where the line passes through grid intersections.
• Calculate the slope of the line using these points.
• Determine the y-intercept by observing where the line crosses the y-axis.
• Compare the calculated slope and intercept with the given equations to find the match.

Let's identify two points on the line. From the graph, we see the line passes through at least two points: $(-3, 0)$ and $(0, 5)$.

Using these points, we calculate the slope $m$:

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 0}{0 - (-3)} = \frac{5}{3}$

Next, observe that the y-intercept (where the line crosses the y-axis) corresponds to $y = 5$ when $x = 0$, so the y-intercept is 5.

Now we can formulate the linear equation based on our calculations:

$y = \frac{5}{3} x + 5$

After calculating the slope and intercept, we compare with the provided options:

• Option 1: $y = 5x$ – Slope and intercept do not match.
• Option 2: $y = -2x + 4$ – Slope and intercept do not match.
• Option 3: $y = \frac{5}{3}x + 5$ – Both slope and intercept match exactly.
• Option 4: $y = 8$ – Not a linear equation of this form.

Thus, the equation that corresponds to the function represented in the graph is:

$y = \frac{5}{3}x + 5$