Answer :
Answer:
The values in the table are proportional with the constant of proportionality [tex]k=2.5[/tex]
For the given table the equation can be written as :
[tex]y=2.5x[/tex]
The value of [tex]y=15[/tex] when [tex]x=6[/tex]
Step-by-step explanation:
From a given data with points [tex](x,y)[/tex] the constant of proportionality [tex]k[/tex] can be calculated as:
[tex]k=\frac{y}{x}[/tex]
For the given data we will find the constant of proportionality [tex]k[/tex] for each point.
1) [tex](1,2.5)[/tex]
[tex]k=\frac{2.5}{1}=2.5[/tex]
2) [tex](2,5)[/tex]
[tex]k=\frac{5}{2.5}=2.5[/tex]
3) [tex](3,7.5)[/tex]
[tex]k=\frac{7.5}{3}=2.5[/tex]
4) [tex](4,10)[/tex]
[tex]k=\frac{10}{4}=2.5[/tex]
We see that for each set of points we get the same value of [tex]k[/tex]. This shows that the values in the table are proportional with the constant of proportionality [tex]k=2.5[/tex]
The equation of [tex]y[/tex] directly proportional to [tex]x[/tex] can be written as :
[tex]y=kx[/tex]
where [tex]k[/tex] is the constant of proportionality
For the given table the equation can be written as :
[tex]y=2.5x[/tex]
To find value of [tex]y[/tex] when [tex]x=6[/tex], we will plugin 6 in place of [tex]x[/tex] in the equation and solve for [tex]y[/tex]
So, we have.
[tex]y=2.5\times6=15[/tex]
So, value of [tex]y=15[/tex] when [tex]x=6[/tex]