2.4 Linear Models

Slope Intercept Form: Linear Modeling

A rental agency rents their equipment for $12 per hour and requires a flat fee of $25. Write a linear model that shows the cost, y in terms of hours rented, x. Y = 12x + 25

Standard Form- Linear Modeling

The marching band holds a fund raiser each year in which they sell t-shirts and sweatshirts. T-shirts cost $7 while sweatshirts cost $15. The band needs to raise $3000. Write a model to show the number of t-shirts and sweatshirts they need to sell to reach their goal. 7x + 15y = 3000

Find slope. What does it represent? The base pay of a water delivery person is $210 per week. He also earns 20% commission. Find slope. What does it represent? Find the y-intercept. What does it represent? Y = .2x + 210

You are sent to the store to buy sliced meat for a party You are sent to the store to buy sliced meat for a party. Roast beef cost $4.29/lb and Turkey cost $3.99/lb. Write an equation to relate the pounds of each you could buy with $30. x = lbs of Roast Beef y = lbs of Turkey 4.29x + 3.99y = 30

Write an equation in standard form to find the minutes someone who weighs 150 lbs would need to bicycle and swim laps in order to burn 300 calories. 10x + 12y = 300

Scatter Plot scatterplot shows the relationship between two sets of data. correlation shows the type of relationship that exist between sets of data.

More with Correlation Positive correlation As x increases, y increases. Negative Correlation As x increases, the y decreases. No Correlation Two sets of data do not relate to each other – one set has nothing to do with the other

A trend line is a line that approximates the relationship between the data sets of a scatterplot. You can use a trend line to make predictions.

Line of Best Fit Give more accurate predictions of lines through use of the graphing calculator.

Example Find the line of best fit. Use your model to predict the wing span when L=20. Use your model to predict how long a hawk is with a wing span of 40 inches. Y = 1.44x + 11.13 39.93 20.05

Let x = 0 represent the beginning year! When YEARS are involved, never use the exact year, use the amount of time passed! Let x = 0 represent the beginning year! Y = 32.33x + 335.33

You Try! Use your model to predict the year that the number of crimes was 6000. Use your model to predict the crime rate in 2009. Y = -248.55x + 5332.82 -2.68 meaning 1992 1853.12

Example Predict the time it will take to travel 30 miles. Predict the speed after 1 hr. Y = 4.56x + 2.83 139.63 12.54