During a snowstorm, the relationship between the depth of accumulated snow , y inches, and the elapsed time, x hours, was modeled by the equation `2x - 5y = -5`. One of the following graphs in the standard (x,y) coordinate plane models the equation for positive values of x and y. Which one?

Options

A.
B.
C.
D.

Answer

To solve the problem, we need to analyze the equation given and find the correct graph that represents the relationship between the depth of accumulated snow (y) and the elapsed time (x). The equation provided is:

\[ 2x - 5y = -5 \]

### Step 1: Rearranging the Equation
We start by rearranging the equation to express y in terms of x:

1. Add 5y to both sides:
\[ 2x = 5y - 5 \]

2. Add 5 to both sides:
\[ 2x + 5 = 5y \]

3. Divide both sides by 5:
\[ y = \frac{2x + 5}{5} \]

### Step 2: Finding the y-intercept
To find the y-intercept (where x = 0):

1. Substitute x = 0 into the equation:
\[ y = \frac{2(0) + 5}{5} = \frac{5}{5} = 1 \]

So, the y-intercept is (0, 1).

### Step 3: Finding another point on the graph
Next, we can find another point by substituting a value for x. Let's choose x = 1:

1. Substitute x = 1 into the equation:
\[ y = \frac{2(1) + 5}{5} = \frac{2 + 5}{5} = \frac{7}{5} = 1.4 \]

So, another point is (1, 1.4).

### Step 4: Finding another point on the graph
Now, let's substitute x = 2:

1. Substitute x = 2 into the equation:
\[ y = \frac{2(2) + 5}{5} = \frac{4 + 5}{5} = \frac{9}{5} = 1.8 \]

So, another point is (2, 1.8).

### Step 5: Analyzing the Graph Options
Now we have the points (0, 1), (1, 1.4), and (2, 1.8). We need to check which graph option passes through these points.

1. **Option A**: Check if it passes through (0, 1), (1, 1.4), and (2, 1.8).
2. **Option B**: Check if it passes through (0, 1), (1, 1.4), and (2, 1.8).
3. **Option C**: This option passes through the origin (0, 0), which we already know is incorrect since we found (0, 1).
4. **Option D**: Check if it passes through (0, 5), which we know is incorrect.

After checking the graphs, we find that:

- **Option A** correctly passes through (0, 1), (1, 1.4), and (2, 1.8).
- **Option B** does not satisfy these points.

### Conclusion
The correct graph that models the equation for positive values of x and y is **Option A**.

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