1. if you use 1/2 cup of sugar, you need 3/4 cup of flour. To find how many cup of flour do you need for 4 cups of sugar, you can use the next proportion:
[tex]\frac{\frac{1}{2}\text{cup of sugar}}{4\text{ cup of sugar}}=\frac{\frac{3}{4}\text{ cup of flour}}{x\text{ cup of flour}}[/tex]Solving for x
[tex]\begin{gathered} \frac{1}{2}\cdot x=\frac{3}{4}\cdot4 \\ x=3\cdot2 \\ x=6 \end{gathered}[/tex]You need 6 cups of flour for the first recipe.
Replacing x = 4 into the equation, we get:
[tex]\begin{gathered} y=\frac{7}{4}\cdot x \\ y=\frac{7}{4}\cdot4 \\ y=7 \end{gathered}[/tex]You need 7 cups of flour for the first recipe.
2. The constant of proportionality of the table is got dividing the values of the variables. Taking for example, 1/2 cup of sugar and 3/4 cup of flour,
[tex]\frac{\frac{3}{4}}{\frac{1}{2}}=\frac{3}{4}\cdot2=3\cdot\frac{2}{4}=3\cdot\frac{1}{2}=\frac{3}{2}[/tex]the constant is 3/2 for the first recipe.
In the second recipe, the constant is 7/4; as can be seen in the equation
The constant relates the number of flour cups needed for 1 cup of sugar