Question

given the equation $y = \frac{1}{3}x$, which of the following are corresponding values of $x$ and $y$?
select all that apply
a $(9,3)$
b $(6,18)$
c $(13,39)$
d $(42,14)$
e $(54,16)$

Explanation:

Step1: Check option a

For the point \((9, 3)\), substitute \(x = 9\) into \(y=\frac{1}{3}x\). Then \(y=\frac{1}{3}\times9 = 3\), which matches the \(y\)-value of the point. So option a is valid.

Step2: Check option b

For the point \((6, 18)\), substitute \(x = 6\) into \(y=\frac{1}{3}x\). Then \(y=\frac{1}{3}\times6 = 2\), which is not equal to \(18\). So option b is invalid.

Step3: Check option c

For the point \((13, 39)\), substitute \(x = 13\) into \(y=\frac{1}{3}x\). Then \(y=\frac{1}{3}\times13=\frac{13}{3}\approx4.33\), which is not equal to \(39\). So option c is invalid.

Step4: Check option d

For the point \((42, 14)\), substitute \(x = 42\) into \(y=\frac{1}{3}x\). Then \(y=\frac{1}{3}\times42 = 14\), which matches the \(y\)-value of the point. So option d is valid.

Step5: Check option e

For the point \((54, 16)\), substitute \(x = 54\) into \(y=\frac{1}{3}x\). Then \(y=\frac{1}{3}\times54 = 18\), which is not equal to \(16\). So option e is invalid.

Answer:

a. \((9, 3)\), d. \((42, 14)\)