Question

use the equation $y = 4.5x + 4$ to complete the following table.

$x$	$y$
2	\boxed{}
4	\boxed{}
6	\boxed{}

is there a proportional relationship between the values of $y$ and $x$ in the table above?
\bigcirc yes, the relationship is proportional.
\bigcirc no, the relationship is not proportional.

Explanation:

Step1: Calculate y for x=1

Substitute $x=1$ into $y=4.5x+4$
$y=4.5(1)+4=8.5$

Step2: Calculate y for x=2

Substitute $x=2$ into $y=4.5x+4$
$y=4.5(2)+4=13$

Step3: Calculate y for x=4

Substitute $x=4$ into $y=4.5x+4$
$y=4.5(4)+4=22$

Step4: Calculate y for x=6

Substitute $x=6$ into $y=4.5x+4$
$y=4.5(6)+4=31$

Step5: Check proportionality

Proportional relationships follow $y=kx$ (no constant term). Our equation has $+4$, so $\frac{y}{x}$ is not constant: $\frac{8.5}{1}=8.5$, $\frac{13}{2}=6.5$, which are not equal.

Answer:

Completed table values:

• When $x=1$, $y=8.5$
• When $x=2$, $y=13$
• When $x=4$, $y=22$
• When $x=6$, $y=31$

Proportional relationship answer:
No, the relationship is not proportional.