Given the data set (5, 9), (13, 12), (23, 16), which of the following equations best represents a line of best fit?
y = three fourthsx − 7
y = four fifthsx + 7
y = three over twox + 7
y = two thirdsx − 7
graph them on paper, and then decide.
Y= 2/3 x -7
To determine which equation best represents the line of best fit for the given data set, we need to calculate the slope and y-intercept of the line. The equation of a straight line is typically written in the form y = mx + b, where m represents the slope and b represents the y-intercept.
Let's calculate the slope using the data points (5, 9), (13, 12), and (23, 16):
First, we calculate the difference in y-coordinates and the difference in x-coordinates between the first two points:
Δy = 12 - 9 = 3
Δx = 13 - 5 = 8
Next, we calculate the slope (m) by dividing the difference in y-coordinates by the difference in x-coordinates:
m = Δy / Δx = 3 / 8
The slope is approximately 0.375.
Let's calculate the y-intercept (b) by substituting one of the data points and the slope into the equation y = mx + b. We'll use the first data point (5, 9):
9 = 0.375 * 5 + b
9 = 1.875 + b
To solve for b, we subtract 1.875 from both sides:
b = 9 - 1.875
b = 7.125
Now that we have the slope (m = 0.375) and the y-intercept (b = 7.125), we can write the equation of the line of best fit:
y = 0.375x + 7.125
Comparing this equation to the given options, we can see that none of the provided equations match the calculated equation.