a) Proportional relationships have the following form:
[tex]y=kx[/tex]Where "k" is the Constant of proportionality.
For this case you have this equation that represents a Proportional relationship:
[tex]y=3x[/tex]So you can identify that the Constant of proportionality is:
[tex]k=3[/tex]b) To make a table you must use different x-values, substitute them into the equation and evaluate, in order to get their corresponding y-values.
- For:
[tex]x=-2[/tex]You get:
[tex]y=3(-2)=-6[/tex]- For:
[tex]x=-1_{}[/tex]You get that:
[tex]y=3(-1)=-3[/tex]- For:
[tex]x=2[/tex][tex]y=3(2)=6[/tex]- For:
[tex]x=4[/tex][tex]y=3(4)=12[/tex]Knowing those coordinates, you can make the following table:
c) Use the table the sketch the graph of the relationship.
You can see in the table that you have the following points:
[tex](-2,-6),(-1,-3),(2,6),(4,12)[/tex]Plot these points on a Coordinate plane. The line must pass through those points (It's important to know that, by definition, the graph of this relationships will always pass through the origin):
The graph of the Proportional relationship is
