Minutes 2 4 6 8
Number of Sit-ups
y 24 36 48
Lynne can do 24 sit-ups in 4 minutes. How many sit-ups can she do in 2 minutes?
(1 point)
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To find out how many sit-ups Lynne can do in 2 minutes, we need to determine the rate at which she is doing sit-ups.
From the given data, we can see that the number of sit-ups is increasing by 12 every 2 minutes.
Therefore, we can calculate the number of sit-ups Lynne can do in 2 minutes using the ratio:
$$\text{Sit-ups in 2 minutes} = \frac{\text{Sit-ups in 4 minutes}}{4} \times 2$$
$$\text{Sit-ups in 2 minutes} = \frac{24}{4} \times 2$$
$$\text{Sit-ups in 2 minutes} = 6 \times 2$$
$$\text{Sit-ups in 2 minutes} = 12$$
Therefore, Lynne can do 12 sit-ups in 2 minutes.
To find out how many sit-ups Lynne can do in 2 minutes, we can use the given data to create a linear equation.
From the data provided, we can see that Lynne does 24 sit-ups in 4 minutes. So, the slope of the line can be calculated as:
slope = (change in y / change in x) = (36 - 24) / (4 - 2) = 12 / 2 = 6
Now that we have the slope, we can use the point-slope form of a linear equation to find the number of sit-ups Lynne can do in 2 minutes.
y - y1 = m(x - x1)
Let's use the point (4, 24) as our reference point.
y - 24 = 6(x - 4)
Simplifying the equation, we get:
y - 24 = 6x - 24
Now, substituting x = 2 into the equation:
y - 24 = 6(2) - 24
Simplifying further, we get:
y - 24 = 12 - 24
y - 24 = -12
Finally, solving for y, we have:
y = -12 + 24
y = 12
So, Lynne can do 12 sit-ups in 2 minutes.
To find the number of sit-ups Lynne can do in 2 minutes, you need to use the given information and calculate the rate at which she performs sit-ups.
From the provided table, we see that in 4 minutes, Lynne can do 24 sit-ups. We can therefore write the following equation to represent the relationship between the number of minutes and the number of sit-ups:
Sit-ups = m * Minutes + b
Where m is the rate at which she performs sit-ups (or the slope of the equation) and b is the number of sit-ups she can do when time is zero (or the y-intercept of the equation).
To determine the value of m, we can use the information given:
m = (Number of Sit-ups2 - Number of Sit-ups1) / (Minutes2 - Minutes1)
= (36 - 24) / (4 - 2)
= 12 / 2
= 6
So the rate at which Lynne performs sit-ups is 6 sit-ups per minute.
Now that we have the value of m, we can plug it into the equation and solve for the number of sit-ups in 2 minutes:
Sit-ups = 6 * 2 + b
To find b, we can use one of the data points from the table. Let's use the first data point (2 minutes and 24 sit-ups):
24 = 6 * 2 + b
24 = 12 + b
Subtracting 12 from both sides of the equation, we get:
b = 24 - 12
b = 12
Now we know that when the time is zero (0 minutes), Lynne can do 12 sit-ups.
Therefore, plugging in the values in the equation, we can calculate the number of sit-ups Lynne can do in 2 minutes:
Sit-ups = 6 * 2 + 12
= 12 + 12
= 24
So Lynne can do 24 sit-ups in 2 minutes.