Question

the scatter plot shows the number of milk cow operations in new mexico from 1975 to 1995. write an equation for the line of best fit. then predict the number of milk cow operations in the year 2005. a. y = - 5x+1900; about 1885 milk cow operations in the year 2005 b. y = - 50x+1900; about 400 milk cow operations in the year 2005 c. y = - 50x+100; about 1400 milk cow operations in the year 2005 d. y = - 5x+100; about 250 milk cow operations in the year 2005

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given two points $(x_1,y_1)=(10,1400)$ and $(x_2,y_2)=(20,900)$.
$m=\frac{900 - 1400}{20 - 10}=\frac{- 500}{10}=-50$.

Step2: Find the y - intercept

We use the point - slope form $y - y_1=m(x - x_1)$ with the point $(x_1,y_1)=(10,1400)$ and $m=-50$.
$y-1400=-50(x - 10)$.
Expand: $y-1400=-50x + 500$.
Add 1400 to both sides: $y=-50x+1900$.

Answer:

b. $y=-50x + 1900$