Question

use the system of equations in a - c to answer the questions.
a use the graphed system of equations to answer 1 - 3.

1. write the equation of each line in slope - intercept form.

a: y = 1x b: y = x

1. what is the solution to the system of equations? (3,10)
2. show work below to prove the solution is correct.

line a(0,4)
line b(0,12)
b the graph shows the cost of a pizza at two restaurants based on the number of toppings ordered. use the graph to answer 4 - 6.

1. write the equation of each line in slope - intercept form.

a: b:

1. what is the solution to the system of equations? (3,12)
2. what does the solution mean in the context of the situation?

c the graph compares the amount of money in two accounts based on the number of weeks each person has been saving. use the graph to answer 7 - 8.

1. what is the solution to the system of equations? (6,300)
2. which statement is true?

a. at 0 weeks, lane and landry will have the same amount of money.
b. after 6 weeks, lane will have more money than landry.
c. lane saves at a rate more than three times that of landry.
d. all of the above.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: For Restaurant A

Let's assume two points on Restaurant A's line: $(0,6)$ and $(2,9)$. The slope $m=\frac{9 - 6}{2-0}=\frac{3}{2}$, and the y - intercept $b = 6$. So the equation is $y=\frac{3}{2}x + 6$.

Step3: For Restaurant B

Let's assume two points on Restaurant B's line: $(0,9)$ and $(2,12)$. The slope $m=\frac{12 - 9}{2 - 0}=\frac{3}{2}$, and the y - intercept $b = 9$. So the equation is $y=\frac{3}{2}x+9$.

Step4: Analyze the solution meaning

The solution $(3,12)$ means that when 3 toppings are ordered, the total cost at both restaurants is $12$.

Answer:

1. A: $y=\frac{3}{2}x + 6$; B: $y=\frac{3}{2}x+9$
2. $(3,12)$
3. When 3 toppings are ordered, the total cost of a pizza at both Restaurant A and Restaurant B is $12$.