The problem is as following:
The graph shows the relationship between the total cost and the number of gift cards that Raj bought for raffle prizes. What would be the cost for 5 of the gift cards? $80, $90, $100 Or $110
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Solution:
The points of the figure represents a straight line
The general form of the straight line is ⇒ y = mx + c
where m is the slope and c is constant
let x ⇒ The number of gifts cards , y ⇒ Total cost (in $)
we will find m and c using the points (1,20) , (2,40)
The slope = m = [tex]\frac{y_{2} - y_{1}}{x_{2}-x_{1}} =\frac{40-20}{2-1} =\frac{20}{1}=20[/tex]
∴ y = 20x + c
Substitute with the point (1,20) ⇒ y = 20 at x = 1
∴ 20 = 20 * 1 + c
∴ 20 = 20 + c
∴ c = 0
∴ The equation of the line ⇒⇒⇒ y = 20x
To find the cost for 5 of the gift cards substitute with x = 5
∴ y = 20 * 5 = 100
So, the cost for 5 of the gift cards = $100
The correct answer is option 3 ⇒⇒⇒ $100
