Evaluate every card against the target constant of proportionality \(k~=~1.5\).
Card A: Equation \(y~=~1.5x\)
Card B: Table with \(x\)-values \(2,~4,~6\) and \(y\)-values \(3,~6,~9\)
Card C: Context: A taxi fare \(y\) is \(\$3\) when the distance \(x\) is \(2~\text{miles}\), and the total fare is proportional to the number of miles.
Card D: Graph passing through the origin and the point \((4,~8)\)
Card E: Equation \(y~=~x~+~1.5\)
Card F: Table with \(x\)-values \(3,~6,~9\) and \(y\)-values \(2,~4,~6\)
Report the complete set of cards with \(k~=~1.5\).
What this problem is really about
Each card must be both proportional and have output divided by input equal to the target constant. We’ll read the coefficient in proportional equations, calculate y over x from every table and context pair, and use rise over run on the origin-crossing graph. An added term or a different quotient prevents a match, even if the target number appears somewhere.