Question

gemi 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 | -20
5 | -10
10 | 0
15 | 10
20 | 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

Explanation:

Step1: Recall slope formula

The 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 take two points from the table, e.g., \((0, -20)\) and \((5, -10)\).

Step2: Calculate slope

Substitute into the formula: \( m=\frac{-10 - (-20)}{5 - 0}=\frac{10}{5} = 2 \).

Step3: Find y - intercept

The y - intercept is the value of \( y \) when \( x = 0 \). From the table, when \( x = 0 \), \( y=-20 \), so the y - intercept is \(-20\).

Answer:

slope: 2, y - intercept: \(-20\)