Question

Create a formula for the points (1,5) , (2,7) , (3,9) , and (4,11) .(1 point)
Responses

y=−2x+3
y equals negative 2 x plus 3

y=2x+3
y equals 2 x plus 3

y=2x−3
y equals 2 x minus 3

y=−2x−3
y equals negative 2 x minus 3

Answer 1

None of the given formulas match the points (1,5), (2,7), (3,9), and (4,11). In order to find the correct formula, we can use the method of linear regression.

First, let's calculate the slope (m) using the formula:

m = (Σ(xy) - n(Σx)(Σy)) / (Σ(x^2) - n(Σx^2))

where Σ represents the sum of a series, Σ(xy) represents the sum of the products of x and y values, Σ(x) represents the sum of x values, Σ(y) represents the sum of y values, Σ(x^2) represents the sum of squared x values, and n represents the number of data points.

For the given points (1,5), (2,7), (3,9), and (4,11):

Σ(x) = 1+2+3+4 = 10
Σ(y) = 5+7+9+11 = 32
Σ(xy) = (1*5) + (2*7) + (3*9) + (4*11) = 5 + 14 + 27 + 44 = 90
Σ(x^2) = (1^2) + (2^2) + (3^2) + (4^2) = 1 + 4 + 9 + 16 = 30
n = 4

Now, we can substitute these values into the slope formula:

m = (90 - 4*10*32) / (30 - 4*10^2)
m = (90 - 1280) / (30 - 400)
m = -1190 / -370
m = 3.22 (rounded to two decimal places)

Next, let's calculate the y-intercept (b) using the formula:

b = (Σy - m(Σx)) / n

Substituting the given values:

b = (32 - 3.22*10) / 4
b = (32 - 32.2) / 4
b = -0.2 / 4
b = -0.05 (rounded to two decimal places)

Finally, we can express the formula in slope-intercept form:

y = mx + b

Substituting the values we found:

y = 3.22x - 0.05

Therefore, the formula for the given points is y = 3.22x - 0.05.