David had a coupon for the grocery store. He started graphing on the x-axis what his total bill would be if he didn’t use the coupon and graphing on the y-axis what his total bill would be if he used the coupon.

Question

Grocery Bill
A graph has bill without coupon on the x-axis and bill with coupon on the y-axis. A line goes through points (2, 0) and (3, 1).

Based on the information in the graph, develop an equation and use it to determine if David’s bill came to $66 after the coupon was applied, how much would his bill have been if he hadn’t used the coupon?
$64
$65
$67
$68

Answer 1

To determine the relationship between the total bill without the coupon (on the x-axis) and the total bill with the coupon (on the y-axis), we first need to formulate the equation based on the provided points.

The given points are:

• Point (2, 0)
• Point (3, 1)

These points give us two pieces of information:

1. When the bill without the coupon is $2, the bill with the coupon is $0.
2. When the bill without the coupon is $3, the bill with the coupon is $1.

Using these points, we can find the slope (m) of the line using the formula:

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

Using points (2, 0) and (3, 1):

\[ m = \frac{1 - 0}{3 - 2} = \frac{1}{1} = 1 \]

Since we have a slope of 1, we can use point-slope form to create the equation for the line. Starting from the point (2, 0):

\[ y - 0 = 1(x - 2) \] \[ y = x - 2 \]

To express this in terms of the total bill with the coupon (y) and without the coupon (x):

\[ y = x - 2 \quad \text{or} \quad x = y + 2 \]

Now, we are given that David’s bill with the coupon (y) is $66, and we want to find his total bill without the coupon (x):

Substituting \(y = 66\) into the equation:

\[ x = 66 + 2 \] \[ x = 68 \]

So, if David's bill came to $66 after the coupon was applied, his total bill would have been $68 before the coupon.

Thus, the final answer is:

$68