Answer :
Since the relationship is proportional, we can express it with the equation
[tex]$$
y = kx,
$$[/tex]
where [tex]$k$[/tex] is the constant of proportionality.
1. Choose one of the data points to find [tex]$k$[/tex]. For example, using the point [tex]$(3, 12)$[/tex], we have
[tex]$$
k = \frac{12}{3} = 4.
$$[/tex]
2. Now, verify that this same value of [tex]$k$[/tex] works for the other points:
- For the point [tex]$(13, 52)$[/tex]:
[tex]$$
k = \frac{52}{13} = 4.
$$[/tex]
- For the point [tex]$(16, 64)$[/tex]:
[tex]$$
k = \frac{64}{16} = 4.
$$[/tex]
- For the point [tex]$(20, 80)$[/tex]:
[tex]$$
k = \frac{80}{20} = 4.
$$[/tex]
Since all points give the same constant [tex]$k = 4$[/tex], the equation that relates [tex]$x$[/tex] and [tex]$y$[/tex] is
[tex]$$
y = 4x.
$$[/tex]
[tex]$$
y = kx,
$$[/tex]
where [tex]$k$[/tex] is the constant of proportionality.
1. Choose one of the data points to find [tex]$k$[/tex]. For example, using the point [tex]$(3, 12)$[/tex], we have
[tex]$$
k = \frac{12}{3} = 4.
$$[/tex]
2. Now, verify that this same value of [tex]$k$[/tex] works for the other points:
- For the point [tex]$(13, 52)$[/tex]:
[tex]$$
k = \frac{52}{13} = 4.
$$[/tex]
- For the point [tex]$(16, 64)$[/tex]:
[tex]$$
k = \frac{64}{16} = 4.
$$[/tex]
- For the point [tex]$(20, 80)$[/tex]:
[tex]$$
k = \frac{80}{20} = 4.
$$[/tex]
Since all points give the same constant [tex]$k = 4$[/tex], the equation that relates [tex]$x$[/tex] and [tex]$y$[/tex] is
[tex]$$
y = 4x.
$$[/tex]