Question

every sunday, lara and her cousins get together for brunch. this week, lara is in charge of making fresh - squeezed orange juice. there is a proportional relationship between the number of oranges lara squeezes, x, and the amount of juice (in ounces) she makes, y.

Explanation:

Assuming the question is to find the constant of proportionality (the rate of juice per orange), here's the solution:

Step1: Identify two points on the line

From the graph, we can see that when \( x = 10 \), \( y = 10 \)? Wait, no, looking at the grid, let's find a clear point. Let's take when \( x = 10 \), wait, maybe better to take \( x = 10 \) (assuming the x - axis grid lines: let's see, when \( y = 20 \), what's \( x \)? Wait, the line passes through (10,10)? No, wait, let's check the slope. Wait, maybe a better point: when \( x = 10 \), \( y = 10 \)? No, wait, let's take two points. Let's say when \( x = 10 \), \( y = 10 \)? No, wait, looking at the graph, when \( y = 20 \), \( x \) is, say, 10? Wait, no, maybe the line has a slope. Wait, let's take (10,20)? No, wait, the grid: each square is, let's assume the x - axis is number of oranges. Let's take two points: (10,20) is not, wait, when \( y = 20 \), \( x \) is, say, 10? Wait, no, let's calculate the slope (constant of proportionality \( k=\frac{y}{x} \)). Let's take a point where \( x \) and \( y \) are clear. Let's take \( x = 10 \), \( y = 20 \)? No, wait, the line goes through (10,20)? Wait, no, the y - axis is ounces. Wait, let's take (10,20) as a point? Wait, no, when \( x = 10 \), \( y = 20 \)? Then \( k=\frac{20}{10} = 2 \). Wait, let's check another point. When \( x = 5 \), \( y = 10 \)? Then \( k=\frac{10}{5}=2 \). When \( x = 10 \), \( y = 20 \), \( k = 2 \). When \( x = 15 \), \( y = 30 \)? Wait, no, the graph shows that for every orange (x), the juice (y) is 2 ounces? Wait, maybe the correct points: let's take (10,20) is not, wait, maybe the line has a slope of 2. Wait, let's do it properly.

Step2: Calculate the constant of proportionality \( k=\frac{y}{x} \)

Take a point on the line, say \( (x,y)=(10,20) \) (assuming the x - axis is number of oranges and y - axis is ounces). Then \( k=\frac{y}{x}=\frac{20}{10} = 2 \). Wait, or if \( x = 5 \), \( y = 10 \), then \( k=\frac{10}{5}=2 \). So the constant of proportionality is 2 ounces per orange.

Answer:

The constant of proportionality is 2 ounces per orange (so the relationship is \( y = 2x \)).