The relationship between the cost charged for the daily boarding of dogs
by the kennel is a directly proportional relationship.
The correct responses are;
1. The dog kennel charges $60 per day is; False
Correct statement; The dog kennel charges $30 per day
2. The equation y = 30·x can represent the graph; True
3. It costs $200 to board a dog for 7 days is; False
Correct statement; It costs $210 to board a dog for 7 days
4.The graph will contain the coordinate point (9, 270); True
Reasons:
Points on the graph of the given graph of the Cost to Number of days are;
(2, 60), (4, 120)
The slope of the graph is [tex]m = \dfrac{120 - 60}{4 - 2} = 30[/tex]
Equation of the graph is therefore; y - 60 = 30·(x - 2)
Which gives;
y = 30·x - 2×30 + 60 = 30·x
The equation of the graph is; y = 30·x
Therefore, the statement;
- 2. The equation y = 30·x can represent the graph is; True
The cost of the dog kennel a day is given by the value of 'y', when x = 1, as
follows;
Cost per day, y = 30 × 1 = 30
The cost per day = $30 per day
Therefore;
- 1. The dog kennel charges $60 per day is; False
The correct statement is; The dog kennel charges $30 per day
- 3. The statement; It costs $200 to board a dog for 7 days is; False
The amount it costs to board a dog for 7 days is y = $30×7 = $210
Therefore, the correct statement is; It costs $210 to board a dog for 7 days
- 4. When x = 9, we have; y = 30 × 9 = 270
Therefore, the statement; the graph will contain the coordinate point (9, 270) is; True
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