Nicholas has some cans at home to donate to the soup kitchen, but he decides to start a can drive at his school to see if other students will help. The table represents the number of cans donated, y, which is dependent on the number of days cans are collected, x.

Question

A 2-column table with 3 rows. Column 1 is labeled x with entries 4, 7, 10. Column 2 is labeled y with entries 955, 1660, 2365.

Find the linear equation that represents the scenario.
y = 235x + 15
y = 4x + 955
y = 15x + 235
y = 3x + 705

Answer 1

To find the linear equation that represents the relationship between the number of days collected (x) and the number of cans donated (y), we can use the data from the table:

• When \( x = 4 \), \( y = 955 \)
• When \( x = 7 \), \( y = 1660 \)
• When \( x = 10 \), \( y = 2365 \)

First, we will calculate the slope (m) of the line using two of the points. The formula for slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Let's choose the points \( (4, 955) \) and \( (7, 1660) \):

\[ m = \frac{1660 - 955}{7 - 4} = \frac{705}{3} = 235 \]

Now that we have the slope \( m = 235 \), we can use the point-slope form of a line \( y - y_1 = m(x - x_1) \) to find the linear equation. We will use the point \( (4, 955) \):

\[ y - 955 = 235(x - 4) \]

Expanding this:

\[ y - 955 = 235x - 940 \]

Adding 955 to both sides:

\[ y = 235x + 15 \]

The linear equation that represents the scenario is:

\[ \boxed{y = 235x + 15} \]

Thus, from the options provided, the correct equation is:

\[ y = 235x + 15 \]