Use the following table of values to find the equation of the trend line for the scatter plot.

x 1 2 3 4 5 6 7 8
y 1.5/2.6/2.2/3 2.9/4.6/ 4.2/5

A.y = –2x + 1
B.y = 0.5x + 1
C.y = x + 2
D.y = 0.5x + 3

I think it is B...? I am not positive

sorry for the way it posted it was more lined up when I typed it

it should be 1-1.5

2-2.6
and so on 3-2.2
4-3
5-2.9

When x is 1, y is 1.5

When x is 2, y is 2.6
When x is 3, y is 2.2
When x is 4, y is 3
When x is 5, y is 2.9
When x is 6, y is 4.6
When x is 7, y is 4.2
When x is 8, y is 5

The numbers aren't adding up :/
Is what I stated above, correct?

A is clearly wrong:
ex. y=-2x +1
1.5 = -2(1)+1
1.5 not= 1

B is also wrong:
ex. y=0.5x +1
1.5 = 0.5(1)+1
1.5=1.5

ex. y=0.5x+1
5=0.5(8)+1
5=4+1
5=5

ex. y=0.5x+1
2.2 = 0.5(3)+1
2.2 not=2.5

It does not work for all set values.

If you do the other 2 you'll see they don't work for all the values as well.

c. y = x + 2
1.5=1+2
1.5 not = 3

d. y = 0.5x + 3
1.5=0.5(1.5)+3
1.5 not = 3.75

I know - I went with B and it was right...it only worked for a few of the values....strange

What exactly is a trend line? I'm thinking it would be B because they're not asking for the exact line. In fact, if it's a scatter plot there wouldn't be a perfect straight line. I think you're right. It's probably B.

To find the equation of the trend line for the scatter plot, we can use the method of linear regression.

Step 1: Calculate the means of the x-values (written as x̄) and the y-values (written as ȳ).

To find x̄, add up all the x-values and divide by the total number of values:
x̄ = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) / 8 = 4.5

To find ȳ, add up all the y-values and divide by the total number of values:
ȳ = (1.5 + 2.6 + 2.2 + 3 + 2.9 + 4.6 + 4.2 + 5) / 8 = 3.1

Step 2: Calculate the slope of the trend line (m).

To find the slope, we need to calculate the numerator and denominator separately.

Numerator: Sum of the x-values multiplied by their respective y-values minus the product of their respective means.
numerator = (1*1.5 + 2*2.6 + 3*2.2 + 4*3 + 5*2.9 + 6*4.6 + 7*4.2 + 8*5) - (8 * 4.5 * 3.1) = 59.7 - 111.6 = -51.9

Denominator: Sum of the x-values squared minus the square of the mean of the x-values.
denominator = (1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 + 8^2) - (8 * 4.5^2) = 204 - 162 = 42

Now, calculate the slope:
m = numerator / denominator = -51.9 / 42 = -1.2357 ≈ -1.24

Step 3: Calculate the y-intercept of the trend line (b).

To find b, use the equation of a straight line y = mx + b, where y and x are the mean values and m is the slope.
3.1 = -1.24 * 4.5 + b
b = 3.1 - (-1.24 * 4.5) = 3.1 + 5.58 = 8.68 ≈ 8.7

Therefore, the equation of the trend line for the scatter plot is:
y = -1.24x + 8.7

Comparing this with the given options, the correct answer is not B. The correct answer is A: y = -2x + 1.