Constant of proportionality from graphs

Google Classroom

Problem

The following graph shows a proportional relationship.

What is the constant of proportionality between $y$y and $x$x in the graph?

$\small{1}$$\small{2}$$\small{3}$$\small{4}$$\small{5}$$\small{6}$$\small{1}$$\small{2}$$\small{3}$$\small{4}$$\small{5}$$\small{6}$$y$$x$

Constant of proportionality $=$equals 

Hint #11 / 4

If the constant of proportionality of a proportional relationship is $k$k, then:

$\maroonD{y}=\greenD{k}\blueD{x}$start color #ca337c, y, end color #ca337c, equals, start color #1fab54, k, end color #1fab54, start color #11accd, x, end color #11accd

Let's pick a point on the graph to get the $\blueD{x}$start color #11accd, x, end color #11accd- and $\maroonD{y}$start color #ca337c, y, end color #ca337c-values. Then we can solve for $\greenD{k}$start color #1fab54, k, end color #1fab54.

Hint #22 / 4

$\small{1}$$\small{2}$$\small{3}$$\small{4}$$\small{5}$$\small{6}$$\small{1}$$\small{2}$$\small{3}$$\small{4}$$\small{5}$$\small{6}$$y$$x$$\left(3,2\right)$

$\maroonD{2}=\greenD{k}\cdot\blueD{3}$start color #ca337c, 2, end color #ca337c, equals, start color #1fab54, k, end color #1fab54, dot, start color #11accd, 3, end color #11accd

Hint #33 / 4

Let's divide both sides of the equation by $3$3 to solve for $\greenD{k}$start color #1fab54, k, end color #1fab54.

$\begin{aligned} \dfrac{\maroonD{2}}{3}&=\dfrac{\greenD{k}\cdot\cancel{\blueD{3}}}{\cancel 3} \\\\ \dfrac{2}{3}&=\greenD{k} \end{aligned}$

Hint #44 / 4

The constant of proportionality between $y$y and $x$x in this graph is $\dfrac{2}{3}$start fraction, 2, divided by, 3, end fraction.