Answer:
[tex]\begin{gathered} \text{slope m =}\frac{7}{3} \\ \text{equation } \\ y=\frac{7}{3}x \end{gathered}[/tex]Graphing the function;
Explanation:
Given that the points (9, 21) and (18, 42) form a proportional relationship.
[tex]y=mx[/tex]where; m = slope.
Given;
[tex]\begin{gathered} (x_1,y_1)=(9,21) \\ (x_2,y_2)=(18,42) \end{gathered}[/tex]Calculating the slope;
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{substituting the given coordinates;} \\ m=\frac{42-21}{18-9} \\ m=\frac{21}{9} \\ m=\frac{7}{3} \end{gathered}[/tex]The slope of the line passing througth the points is;
[tex]\frac{7}{3}[/tex]So, the equation of the proportional relationship is;
[tex]y=\frac{7}{3}x[/tex]Graphing the function;
