Question

On April 24, 1921, 76 in. of snow fell in one 24 h period in Silver Lake, Colorado. If the snow fell at a steady pace, then the equation y = 19/6x models the number of inches of snow, y, that fell x hours after the start of the 24 h period.
Determine if the point (3, 9.5) lies on the line y = 19/6x.
Enter numbers into the boxes.

y = 19/6x

__ = 19/6 ⋅ __

__ = __

Answer 1

The first box is incorrect.

Answer 2

To determine if the point (3, 9.5) lies on the line given by the equation \( y = \frac{19}{6}x \), we first need to substitute \( x = 3 \) into the equation and check if it produces \( y = 9.5 \).

Substituting \( x = 3 \):

\[
y = \frac{19}{6} \cdot 3
\]

Calculating \( \frac{19}{6} \cdot 3 \):

\[
y = \frac{19 \cdot 3}{6} = \frac{57}{6} = 9.5
\]

Now we can fill in the boxes:

1. The first box will be the \( x \) value we used: **3**
2. The second box will be the \( x \) value in the equation: **3**
3. The third box will be \( y \) from the point: **9.5**
4. The fourth box will be the calculated \( y \): **9.5**

So, it can be filled in as follows:

y = \(\frac{19}{6} \cdot 3\)

3 = \(\frac{19}{6} \cdot 3\)

9.5 = 9.5

Since both sides are equal, (3, 9.5) does indeed lie on the line \( y = \frac{19}{6}x \).

Answer 3

Apologies for that oversight. Let's break it down again clearly to fill in the boxes correctly.

We are given the equation:

\[
y = \frac{19}{6}x
\]

We want to verify whether the point (3, 9.5) lies on the line formed by the equation.

1. We substitute \( x = 3 \) into the equation:

\[
y = \frac{19}{6} \cdot 3
\]

2. Now, let's calculate \( \frac{19}{6} \cdot 3 \):

\[
y = \frac{19 \cdot 3}{6} = \frac{57}{6} = 9.5
\]

Now we proceed to fill in the boxes:
1. First box (the value of \( y \) calculated): **9.5** (this is the left side of the equation).
2. Second box (the value of \( x \) where \( y \) becomes): **3**.
3. Third box (the \( y \) value from the point provided): **9.5**.
4. Fourth box (the calculated \( y \) using the equation): **9.5**.

So, the complete filling should be:

y = \(\frac{19}{6} \cdot 3\)

9.5 = \(\frac{19}{6} \cdot 3\)

9.5 = 9.5

Thank you for your patience, and please let me know if anything else needs clarification!