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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.

Respuesta :

LRev

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:

[tex]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[/tex]

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

[tex]y-y_1=m(x-x_1)[/tex] point-slope form

[tex]y=mx+b[/tex] slope-intercept form

[tex]y-y_1=m(x-x_1)\\y-51.7=2.2(x-0)\\y-51.7=2.2x\\y=2.2x+51.7[/tex]

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

[tex]y=2.2x+51.7\\y=2.2(6)+51.7\\y=13.2+51.7\\y=64.9[/tex] billions

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