Math  /  Algebra

QuestionLesson Check Do you know HOW?
1. Is (2,4)(2,4) a solution of the equation y=x2y=x-2 ?
2. Is (3,9)(-3,-9) a solution of the equation y=3xy=3 x ?
3. Drinks at the fair cost $2.50\$ 2.50. Use a table, an equation, and a graph to represent the relationship between the number of drinks bought and the cost.
4. Exercise On a treadmill, you burn 11 Cal in 1 min , 22 Cal in 2 min,33Cal2 \mathrm{~min}, 33 \mathrm{Cal} in 3 min , and so on. How many Calories do you burn in 10 min ?

Do you UNDERSTAND? MATHEMATICAL PRACTICES
5. Vocabulary Describe the difference between inductive reasoning and deductive reasoning. (C) 6
6. Compare and Contrast How is writing an equation to represent a situation involving two variables similar to writing an equation to represent a situation involving only one variable? How are they different? (C) 7. Reasoning Which of (3,5),(4,6),(5,7)(3,5),(4,6),(5,7), and (6,8)(6,8) are solutions of y=x+2y=x+2 ? What is the pattern in the solutions of y=x+2y=x+2 ?

Practice and Problem-Solving Exercises MATHEMATICAL PRACTICES (A) Practice
Tell whether the given equation has the ordered pair as a solution. ( See Problem
8. y=x+6;(0,6)y=x+6 ;(0,6)
9. y=1x;(2,1)y=1-x ;(2,1)
10. y=x+3;(4,1)y=-x+3 ;(4,1)
11. y=6x;(3,16)y=6 x ;(3,16)
12. x=y;(3.1,3.1)-x=y ;(-3.1,3.1)
13. y=4x;(2,8)y=-4 x ;(-2,8)
14. y=x+23;(1,13)y=x+\frac{2}{3} ;\left(1, \frac{1}{3}\right)
15. y=x34;(2,114)y=x-\frac{3}{4} ;\left(2,1 \frac{1}{4}\right)
16. x5=y;(10,2)\frac{x}{5}=y ;(-10,-2)

Studdy Solution

STEP 1

What is this asking? We're going to explore how to figure out if given points are solutions to equations and how to represent relationships between variables using tables, equations, and graphs, focusing on problem number 3 about the cost of drinks at a fair. Watch out! Make sure you understand the difference between an ordered pair (x,y)(x, y) and plugging values into an equation.
Don't mix up your *x*'s and *y*'s!

STEP 2

1. Set up the table
2. Define the relationship
3. Create the equation
4. Sketch the graph

STEP 3

Let's **start** by creating a table with two columns: one for the **number of drinks** bought (xx) and one for the **total cost** (yy).

STEP 4

Let's put in some values.
If you buy **zero** drinks, it costs $0\$0.
If you buy **one** drink, it costs $2.50\$2.50.
If you buy **two** drinks, it costs $5.00\$5.00, and so on.
| Number of Drinks (xx) | Total Cost (yy) | |---|---| | 0 | $0.00\$0.00 | | 1 | $2.50\$2.50 | | 2 | $5.00\$5.00 | | 3 | $7.50\$7.50 |

STEP 5

Notice that the **total cost** (yy) is always the **number of drinks** (xx) *multiplied* by $2.50\$2.50.
This is our **key relationship**!

STEP 6

We can write this relationship as an equation: y=2.50xy = 2.50 \cdot x, where yy is the **total cost** and xx is the **number of drinks**.

STEP 7

Draw a graph with the **number of drinks** (xx) on the horizontal axis and the **total cost** (yy) on the vertical axis.

STEP 8

Plot the points from our table: (0,0)(0, 0), (1,2.50)(1, 2.50), (2,5.00)(2, 5.00), and (3,7.50)(3, 7.50).

STEP 9

Since the cost increases at a **constant rate**, we can connect these points with a **straight line**.
This line represents all possible combinations of drinks and their corresponding costs.
Extend the line beyond the plotted points to show that the relationship continues for any number of drinks.

STEP 10

The table, equation y=2.50xy = 2.50 \cdot x, and graph (a straight line passing through the plotted points (0,0)(0,0), (1,2.50)(1, 2.50), (2,5.00)(2, 5.00), (3,7.50)(3, 7.50) and extending further) all represent the relationship between the number of drinks bought and the total cost.

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