### Home > CCAA > Chapter 10 Unit 11 > Lesson CC3: 10.1.3 > Problem10-43

10-43.

Which table or tables below show a proportional relationship? Justify your answers.

1. $\begin{array}{c|c|c|c|c|c|c|c} \quad x \quad & \quad 5 \quad & \quad 7 \quad & \quad 9 \quad & \;\; -8 \;\; & \quad 0 \quad & \quad 11 \quad & \quad 15 \quad \\ \hline \quad y \quad & 9 & 13 & 17 & -17 & -19 & 21 & 29 \end{array}$

2. $\begin{array}{c|c|c|c|c|c|c|c} \quad x \quad & \quad 7 \quad & \;\;\, 14 \;\;\, & \;\;\; 91 \;\;\; & \quad 9 \quad & \;\, -12 \;\, & \;\, -36 \;\, & \quad 81 \quad \\ \hline \quad y \quad & 2\frac{1}{3} & 4\frac{2}{3} & 30\frac{1}{3} & 3 & -4 & -12 & 27 \end{array}$

3. $\begin{array}{c|c|c|c|c|c|c|c} \quad x \quad & \quad -3 \quad & \quad -10 \quad & \quad \; 0 \quad \; & \quad 10 \quad & \quad \; 5 \quad \; & \quad 4 \quad & \quad \frac{1}{2} \quad & \;\; -\frac{3}{2} \;\; \\ \hline \quad y \quad & -27 & -1000 & 0 & 1000 & 125 & 48 & \frac{1}{8} & -\frac{27}{4} \end{array}$

A proportional equation can be written using an equation of the form $y = kx$.

Based on the equation above, a relationship that is proportional must contain the point $(0,0)$ and have a constant rate of growth represented by a constant, $k$.

Which of these tables has these attributes?

Rearranging the ordered pairs so the $x$-values are listed from smallest to largest $x$-values may be helpful.

Table (b) could contain the point $\left(0,0\right)$ and grows at a constant rate.