Which equation models the relationship between the number of hours, x, of the snowstorm, and the number of inches of snow, y, on the ground?

Steps to Solve

1. Identify the relationship in the graph

From the graph, we see a linear relationship between the number of hours of the snowstorm ($x$) and the inches of snow on the ground ($y$). The graph shows that as $x$ increases, $y$ increases at a constant rate.

2. Determine the slope of the line

To find the slope ($m$) of the line, we can use two points from the graph. Let's use the points (0, 3) and (5, 30):

• The change in $y$ (rise) is $30 - 3 = 27$.
• The change in $x$ (run) is $5 - 0 = 5$.

Thus, the slope can be calculated as: $$ m = \frac{\text{rise}}{\text{run}} = \frac{27}{5} = 5.4 $$

3. Write the equation in point-slope form

Using one of the points, say (0, 3), in the point-slope form $y - y_1 = m(x - x_1)$: $$ y - 3 = 5.4(x - 0) $$ which simplifies to: $$ y = 5.4x + 3 $$

4. Match to the provided equations

Looking at the choices provided, we need to express the slope in a simpler form for comparison. The slope of $5.4$ can be approximated as $\frac{27}{5}$: $$ y = \frac{27}{5}x + 3 $$

Now we can see which option corresponds:

• A: $y = 3x + 3$ (not a match)
• B: $y = \frac{1}{3}x + 3$ (not a match)
• C: $y = 3x + 18$ (not a match)
• D: $y = \frac{1}{3}x + 18$ (not a match)

Since none of the options provided reflect our derived equation, we need to identify if there are adjustments needed based on the context.