Graphing Equations Quick Check

Question

5 of 5 5 of 5 Items

An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 4 right parenthesis and left parenthesis 1 comma negative 1 right parenthesis.

An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 1 right parenthesis and left parenthesis 1 comma negative 4 right parenthesis.






Question
You are baking a cake. For every three cups of flour, you need to add two eggs. Write an equation for the relationship between the number of eggs, y
, and the amount of flour, x
. Distinguish whether this is a proportional or nonproportional situation.(1 point)
Responses

y=2x+3

, nonproportional
y equals 2 x plus 3 , nonproportional
y=23x
, proportional
y equals Start Fraction 2 over 3 End Fraction x , proportional
y=3x+2
, nonproportional
y equals 3 x plus 2 , nonproportional
y=32x
, proportional

Answer 1

To write the equation that represents the relationship between the number of eggs \( y \) and the amount of flour \( x \), we start with the information given: for every 3 cups of flour, you need to add 2 eggs.

This means that the ratio of eggs to flour is 2 eggs for every 3 cups of flour. In mathematical terms, we can express this as:

\[ \frac{y}{x} = \frac{2}{3} \]

From this, we can derive the equation relating \( y \) and \( x \):

\[ y = \frac{2}{3} x \]

This equation represents a proportional relationship because it is of the form \( y = kx \) where \( k \) (the constant of proportionality) is \( \frac{2}{3} \).

So the correct response is: \( y = \frac{2}{3}x \), proportional.