Precalculus linear model

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 (1998,60.6). let x represent the year, where x=0 represents 1994, x=1 represents 1995, and so on, and let y represent the egg production (in billions). predict egg production in 2000. what is the linear model for this data?

year-egg production

1994-51.7

1995-52.6

1996-54.5

1997-57.4

1998-60.6

1999-64.1

2000-69.8

Answer 1

To find the linear equation, you need the slope and the y intercept.

To find the slope:

m=(y₂-y₁)/(x₂-x₁)

m=(60.6-51.7)/(4-0) = 8.9/4 = 2.225

The y intercept is the point where x=0, which is 51.7

Bringing these together, the equation would be

y=2.225x+51.7

Answer 2

Linear model is y = mx + b

So in year 1994, or x = 0, there was 51.7 billion eggs produced. This means that the y intercept is 51.7 billion, or b = 51.7.

m is the slope of the line. You need to find out the difference of egg production for change of y (numerator) and x is always 1 year. I suspect that this is anticipating that you are using a calculator to find the line of best fit. If you find the average rate of change over time, your prediction will be the already provided answer in the table.

2000 - 1999 = 69.8 - 64.1 = 5.7

1999 - 1998 = 64.1 - 60.6 = 3.5

etc.

or 2000 - 1994 = 69.8 - 51.7 = 18.1 divided by 6 years = 3.017 per year

then y = 3.017x + 51.7

y = 69.8 billion eggs

In a calculator, enter the data into a table, but use years of 0, 1, 2, etc. Then CALC, then LinReg for Linear Regression. It will give you an equation in y = mx + b format.