Gerri purchases a coupon book with discounts for her favorite coffee shop. Every coupon for the coffee shop offers the same discount. The table shows her total savings, y, based on the number of coupons, x, used from the book.

Question

A table showing Coffee Shop Coupon Savings with 2 columns and 6 rows. The first column, x, has the entries, 0, 5, 10, 15, 20. The second column, y, has the entries. negative 20, negative 10, 0, 10, 20.
What are the slope and y-intercept of the line represented by the points shown in the table?

slope: 2, y-intercept: –20
slope: 2, y-intercept: 10
slope: 5, y-intercept: –20
slope: 5, y-intercept: 10

Answer 1

To find the slope and y-intercept from the data provided, we first observe the values in the table:

• When \( x = 0 \), \( y = -20 \)
• When \( x = 5 \), \( y = -10 \)
• When \( x = 10 \), \( y = 0 \)
• When \( x = 15 \), \( y = 10 \)
• When \( x = 20 \), \( y = 20 \)

Next, we can determine the slope (m) using the formula:

\[ m = \frac{\Delta y}{\Delta x} \]

Choose two points from the table to calculate the slope. Let's use the points (0, -20) and (5, -10):

\[ \Delta y = -10 - (-20) = 10 \] \[ \Delta x = 5 - 0 = 5 \]

Now, plug these values into the slope formula:

\[ m = \frac{10}{5} = 2 \]

Next, we find the y-intercept. The y-intercept can be identified directly from the first value of \( y \) when \( x = 0 \), which is \( -20 \).

So, we have:

• Slope \( m = 2 \)
• Y-intercept \( b = -20 \)

Thus, the correct answer is:

slope: 2, y-intercept: -20