Write a prediction line (equation of line of best fit) for the points in the table:
x 2 4 6
y 7 13 19
Show all work! List points then write an equation in y = mx+b form.
Use the prediction equation to predict the y value for x = 25.
note that the slope is 6/2 = 3
So, use the line y=3x+1
To find the equation of the line of best fit, we will start by finding the slope (m) and y-intercept (b) using the given points.
First, let's list the given points from the table:
(2, 7), (4, 13), (6, 19)
We can set up three equations using the slope formula:
m = (y2 - y1) / (x2 - x1)
Let's use the first two points, (2, 7) and (4, 13):
m = (13 - 7) / (4 - 2) = 6 / 2 = 3
Now, using the slope-intercept form of a line, y = mx + b, we can substitute the slope (m) and one of the points (x, y) to solve for b.
Using the point (4, 13):
13 = 3(4) + b
13 = 12 + b
b = 13 - 12
b = 1
So, the equation of the line of best fit is:
y = 3x + 1
To predict the y value for x = 25, we can substitute x = 25 into the equation:
y = 3(25) + 1
y = 75 + 1
y = 76
Therefore, the predicted y value for x = 25 is 76.