Question

melanie buys 2 shells for $0.80. rosi buys 3 shells for $1.20. carlos buys 4 shells for $1.60. the relationship between the number of shells, x, and the cost of the shells, y, is proportional and can be represented by the equation y = 0.40x.
determine if the following points or graphs can be represented by the equation y = 0.40x.
(2,0.80) (3,1.20) (1,0.20) (4,1.60)
two graphs of gift shop shells with x-axis number of shells and y-axis cost ($)
can be represented by the equation y = 0.40x
can not be represented by the equation y = 0.40x

Explanation:

Step1: Check the points

For a point \((x,y)\) to satisfy \(y = 0.40x\), substitute \(x\) into the equation and see if \(y\) matches.

• For \((2,0.80)\): \(y=0.40\times2 = 0.80\), matches.
• For \((3,1.20)\): \(y = 0.40\times3=1.20\), matches.
• For \((1,0.20)\): \(y=0.40\times1 = 0.20\), matches.
• For \((4,1.60)\): \(y=0.40\times4 = 1.60\), matches.

Step2: Check the first graph

The first graph passes through \((0,0)\) (proportional relationship starts at origin) and the points \((2,0.80)\), \((3,1.20)\), \((4,1.60)\) which we saw satisfy the equation. So it represents \(y = 0.40x\).

Step3: Check the second graph

The second graph does not pass through \((0,0)\) (starts at \(x = 1\) or later), while \(y=0.40x\) when \(x = 0\) has \(y=0\). So it does not represent the equation.

Answer:

• Can be represented by the equation \(y = 0.40x\): \((2,0.80)\), \((3,1.20)\), \((1,0.20)\), \((4,1.60)\), the first "Gift Shop Shells" graph.
• Can not be represented by the equation \(y = 0.40x\): the second "Gift Shop Shells" graph.