Question

Identify the constant of proportionality for each graph and write equations

Answer 1

k=2, y=2x

K=7, y=7x

k=1/3, y=x/3

Explanation

When two variables are directly or indirectly proportional to each other, then their relationship can be described as y = kx

so, to find the constant we need

$\begin{gathered} y=kx \\ \text{divide both sides by x} \\ \frac{y}{x}=\frac{kx}{x} \\ \frac{y}{x}=k \end{gathered}$

therefore, to find k just take a point from the line and divide y by x,

hence

Step 1

graph 6

take a point

P=(2,4)

now, replace to find k

$\begin{gathered} k=\frac{4}{2} \\ k=2 \end{gathered}$

therefore, for 6 the constant is 2

and the equation is

$y=2x$

Step 2

graph 7

point=(3,21)

replace

$\begin{gathered} k=\frac{y}{x} \\ k=\frac{21}{3} \\ k=7 \end{gathered}$

therefore, for 7 the constant is 7

$\begin{gathered} \text{and the equation would be } \\ y=7x \end{gathered}$

Step 3

Finally, graph 8

point =(9,3)

replace

$\begin{gathered} k=\frac{3}{9} \\ k=\frac{1}{3} \end{gathered}$

therefore, for 8 the constant is 1/3

and the equation would be

$y=\frac{x}{3}$

I hope this helps you