Question

sandra is making popcorn balls for movie night with her friends. the amount of sugar sandra needs depends on the amount of popcorn she uses. this situation can be modeled as a linear relationship. what does the slope of the line tell you about the situation? sandra needs 1 tablespoon of sugar for every cup of popcorn. sandra needs 1 tablespoon of sugar for every 3 cups of popcorn. sandra needs 2 tablespoons of sugar for every 3 cups of popcorn. sandra needs 3 tablespoons of sugar for every 2 cups of popcorn.

Explanation:

Step1: Recall slope formula

The slope \( m \) of a line is given by \( m=\frac{\Delta y}{\Delta x} \), where \( \Delta y \) is the change in \( y \) (tablespoons of sugar) and \( \Delta x \) is the change in \( x \) (cups of popcorn).

Step2: Choose two points

From the graph, let's take two points, e.g., \( (0,0) \) and \( (3,2) \) (or other points like \( (6,4) \), \( (9,6) \)). Using \( (0,0) \) and \( (3,2) \):
\( \Delta y = 2 - 0 = 2 \) (tablespoons of sugar), \( \Delta x = 3 - 0 = 3 \) (cups of popcorn).
So slope \( m=\frac{2}{3} \)? Wait, no, wait, looking at \( (3,2) \): when \( x = 3 \) (cups of popcorn), \( y = 2 \) (tablespoons of sugar). Wait, another point: \( (6,4) \): \( x = 6 \), \( y = 4 \). So \( \Delta y = 4 - 2 = 2 \), \( \Delta x = 6 - 3 = 3 \)? No, wait, let's take \( (3,2) \) and \( (6,4) \). Then \( \Delta y = 4 - 2 = 2 \), \( \Delta x = 6 - 3 = 3 \)? No, wait, \( y \) is tablespoons of sugar, \( x \) is cups of popcorn. Wait, when \( x = 3 \), \( y = 2 \); when \( x = 6 \), \( y = 4 \); when \( x = 9 \), \( y = 6 \). So the slope is \( \frac{y}{x}=\frac{2}{3} \)? Wait, no, wait the options: let's check the last option? Wait no, wait the third option: "Sandra needs 2 tablespoons of sugar for every 3 cups of popcorn" – because slope is \( \frac{2}{3} \), meaning for 3 cups (Δx=3), Δy=2. Wait, let's re - calculate. Let's take \( x = 3 \), \( y = 2 \); \( x = 6 \), \( y = 4 \). So from \( x = 3 \) to \( x = 6 \) (Δx = 3), \( y \) goes from 2 to 4 (Δy = 2). So slope is \( \frac{2}{3} \), which means for every 3 cups of popcorn (Δx = 3), she needs 2 tablespoons of sugar (Δy = 2). So the correct option is "Sandra needs 2 tablespoons of sugar for every 3 cups of popcorn".

Answer:

Sandra needs 2 tablespoons of sugar for every 3 cups of popcorn.