Question

the chart to the right shows a countrys annual egg production. model the data in the chart with a linear function, using the points (0,51.7) and (4,60.2). let x = 0 represent 1994, x = 1 represent 1995, and so on, and let y represent the egg production (in billions). predict egg production in 2000. how does the result compare to the actual data given in the table, 69.7?

the linear model for the data is
(type an equation using x as the variable. type your answer in slope - intercept form. use integers or decimals for any numbers in the equation. round to the nearest thousandth as needed.)

the table is:

year	egg production (in billions)
1995	52.5
1996	54.3
1997	57
1998	60.2
1999	63.8
2000	69.7

Explanation:

Step1: Calculate the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Using the points (0, 51.7) and (4, 60.2), we have $x_1 = 0$, $y_1 = 51.7$, $x_2 = 4$, $y_2 = 60.2$.
So, $m = \frac{60.2 - 51.7}{4 - 0} = \frac{8.5}{4} = 2.125$.

Step2: Determine the y-intercept (b)

The slope-intercept form is $y = mx + b$. We know $m = 2.125$ and when $x = 0$, $y = 51.7$. So, substituting $x = 0$ and $y = 51.7$ into $y = mx + b$, we get $51.7 = 2.125(0) + b$, which means $b = 51.7$.

Step3: Write the linear equation

Substituting $m = 2.125$ and $b = 51.7$ into the slope-intercept form, we get $y = 2.125x + 51.7$.

Answer:

The linear model for the data is $y = 2.125x + 51.7$