Question

Question 111 ptsYou are asked to write an equation for the line of best fit for the scatter plot shown at the right without the use of a graphing calculator. What should you do first?

Answer 1

Step-by-step explanation: write an equation for the line of best fit for the given scatter plot, the first step is to find the slope of the line. The slope represents the rate of change between two points on the line.

To find the slope, we can choose any two points on the scatter plot. In this case, the options given are (4,6) and (5,8), or (1,2) and (9,12).

Let's calculate the slope using the points (4,6) and (5,8):

Slope = (change in y) / (change in x)

The change in y is 8 - 6 = 2, and the change in x is 5 - 4 = 1.

Therefore, the slope using (4,6) and (5,8) is 2/1 = 2.

Now let's calculate the slope using the points (1,2) and (9,12):

Slope = (change in y) / (change in x)

The change in y is 12 - 2 = 10, and the change in x is 9 - 1 = 8.

Therefore, the slope using (1,2) and (9,12) is 10/8 = 1.25.

Comparing the two slopes, 2 and 1.25, we can conclude that the slope of 2 provides a more representative straight line for the scatter plot.

Therefore, the first step to write an equation for the line of best fit is to find the slope using the points (4,6) and (5,8).

Answer 2

step 1

Find two points that you think will be on the "best-fit" line

so

I take (1,2) and (9,12)

step 2

Find the slope

m=(12-2)/(9-1)

m=10/8

m=1.25

step 3

Find the equation of the line in slope intercept form

y=mx+b

we have

m=1.25

point (1,2)

substitute

2=1.25(1)+b

solve for b

b=2-1.25

b=0.75

therefore

the equation of the line is

y=1.25x+0.75