Question

the table shows a proportional relationship between the cups of flour a baker uses and the number of cookies made. use the table to answer parts a through c.

Explanation:

Step1: Calculate the unit rate

The unit rate \(k\) (number of cookies per cup of flour) is found by \(\frac{y}{x}\). For \(x = 3,y=54\), \(k=\frac{54}{3}=18\); for \(x = 5,y = 90\), \(k=\frac{90}{5}=18\); for \(x=7,y = 126\), \(k=\frac{126}{7}=18\). The equation of the proportional relationship is \(y = 18x\).

Step2: Check the slope of the lines

The slope \(m\) of a line \(y=mx\) (since \(b = 0\) for proportional relationships) in a graph.

• For option A: When \(x = 1\), \(y\approx67\) (not \(18\times1 = 18\))
• For option B: When \(x = 1\), \(y\approx100\) (not \(18\times1=18\))
• For option C: When \(x = 1\), \(y = 18\) (since if \(x = 5,y=90\), slope \(m=\frac{90 - 0}{5-0}=18\))
• For option D: When \(x=2\), \(y = 50\) (not \(18\times2 = 36\))

Answer:

C.