Question

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. Coffee Shop Coupon Savings x y 0 -16 4 -8 8 0 16 8 20 16 (2 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. What are the slope and y-intercept of the line represented by the points shown in the table? Slope: Response area y-intercept: Response area  

Answer 1

To find the slope and y-intercept from the data provided in the table, we can examine the changes in the values of \(y\) (savings) with respect to \(x\) (number of coupons used).

1. Calculating the Slope (m): The slope can be computed using the formula: \[ m = \frac{\Delta y}{\Delta x} \] By picking two points, for example (4, -8) and (8, 0):

   • Change in \(y\): \(0 - (-8) = 8\)
   • Change in \(x\): \(8 - 4 = 4\)

   Thus, the slope \(m\) is: \[ m = \frac{8}{4} = 2 \]

2. Calculating the y-intercept: The y-intercept is the value of \(y\) when \(x = 0\). From the table, when \(x = 0\), \(y = -16\). This means the y-intercept is: \[ \text{y-intercept} = -16 \]

Summary:

• Slope: 2
• y-intercept: -16