Answer:
The equation is [tex]y=0.4x[/tex]
The y coordinate of point (6 1/2, y) is y=2 3/5
Step-by-step explanation:
Let us first convert everything to decimal numbers:
[tex](5\frac{5}{8},2\frac{1}{4} )=(5.625,2.25)[/tex]
[tex]6\frac{1}{2} =6.5[/tex]
In a proportional relationship
[tex]\frac{y_1}{x_1} =\frac{y_2}{x_2}[/tex]
For the set of points [tex](5\frac{5}{8},2\frac{1}{4} )[/tex]
[tex]\frac{y_1}{x_1}=\frac{2.25}{5.625}=0.4[/tex]
now this must equal [tex]\frac{y_2}{x_2}[/tex]:
[tex]0.4=\frac{y_2}{x_2}=\frac{y_2}{6.5}\\y_2=0.4*6.5=2.6\:\:\:or\:as\:a\:mixed\:fraction\:\:\:2\frac{3}{5}[/tex]
Now for a proportional relationship the equation is
[tex]y=kx[/tex]
where [tex]k[/tex] is the common ratio between [tex]x[/tex] and [tex]y[/tex] (officially called the 'constant of proportionality').
Now in our case the common ratio is 0.4; therefore
[tex]y=0.4x.[/tex]
