Questions: Philip grows alfalfa on his farm. In the summer, he uses a tractor to harvest the fields before turning the alfalfa into bales of hay. This scatter plot shows how many acres of alfalfa he harvested each time last summer and how long it took. The scatter plot also shows the line of best fit. The equation for the line of best fit is y=3x+1. According to the equation, which of these statements is true? Philip would likely be able to harvest about 1 acre in 3 hours. Philip would likely be able to harvest about 19 acres in 6 hours.

Philip grows alfalfa on his farm. In the summer, he uses a tractor to harvest the fields before turning the alfalfa into bales of hay. This scatter plot shows how many acres of alfalfa he harvested each time last summer and how long it took. The scatter plot also shows the line of best fit.

The equation for the line of best fit is y=3x+1. According to the equation, which of these statements is true?

Philip would likely be able to harvest about 1 acre in 3 hours.

Philip would likely be able to harvest about 19 acres in 6 hours.

Transcript text: Philip grows alfalfa on his farm. In the summer, he uses a tractor to harvest the fields before turning the alfalfa into bales of hay. This scatter plot shows how many acres of alfalfa he harvested each time last summer and how long it took. The scatter plot also shows the line of best fit. The equation for the line of best fit is $y=3 x+1$. According to the equation, which of these statements is true? Philip would likely be able to harvest about 1 acre in 3 hours. Philip would likely be able to harvest about 19 acres in 6 hours.

Solution

Solution Steps

Step 1: Analyze the given equation

The equation for the line of best fit is given as $y = 3x + 1$, where $y$ represents the acres harvested and $x$ represents the time in hours.

Step 2: Evaluate the first statement

The first statement says Philip would likely be able to harvest about 1 acre in 3 hours. Here, $y = 1$ and $x = 3$. Plugging these values into the equation, we get $1 = 3(3) + 1$, which simplifies to $1 = 10$. This is not true, so the first statement is false.

Step 3: Evaluate the second statement

The second statement says Philip would likely be able to harvest about 19 acres in 6 hours. Here, $y = 19$ and $x = 6$. Plugging these values into the equation, we get $19 = 3(6) + 1$, which simplifies to $19 = 19$. This is true, so the second statement is true.