Question

The chart to the right shows a​ country's annual egg production. Model the data in the chart with a linear​ function, using the points ​(1994​,51.7​) and ​(1998​,60.5​). Let x represent the​ year, where xequals0 represents 1994​, xequals1 represents 1995​, and so​ on, and let y represent the egg production​ (in billions). Predict egg production in 2000.

Answer 1

Answer:

64.9  billions

Step-by-step explanation:

Change the points to match the definition given for the representation of the years, the first point (1994,51.7) becomes (0,51.7) and the second (1998,60.5) now is (4,60.5).

Find the slope m of the linear function using the two points and the formula:

$m=\frac{y_2-y_1}{x_2-x_1} \\m=\frac{60.5-51.7}{4-0} \\m=\frac{8.8}{4} =2.2$

Use the point-slope form of the linear equation to find the slope-intercept form:

$y-y_1=m(x-x_1)$ point-slope form

$y=mx+b$ slope-intercept form

$y-y_1=m(x-x_1)\\y-51.7=2.2(x-0)\\y-51.7=2.2x\\y=2.2x+51.7$

2000 is represented by x=6, using the slope-intercept form solve for y (egg production in billions):

$y=2.2x+51.7\\y=2.2(6)+51.7\\y=13.2+51.7\\y=64.9$ billions