Warm Up

Finding the Equation of a Line

y = 1.5x + 12 What we already know: We know the Equation of a Line: We know how to interpret the y – intercept. We know how to interpret the slope. y = mx + b Example Every year Natasha grows 1.5 inches. She was 12 inches long when she was born. y = 1.5x + 12

What if we don’t have an equation or graph?! Sometimes we are given two points and we are asked to find the equation. When this happen we need to find m and b so that we can write the equation! USE THE CALCULATOR!

Let’s do an example together! Find the equation of the line through the points (2, 5) and (6, 7). The Equation of the line is y = .5x + 4.

Examples: Find the Equation through the given Points. 1. (3, 6) and (-1, -2) The Equation of the line is y = 2x + 0.

Examples: Find the Equation through the given Points. 2. (10, 5) and (2, 4) The Equation of the line is y = .125x + 3.75.

Examples: Find the Equation through the given Points. 3. (-3, 0) and (1, 5) The Equation of the line is y = 1.25x + 3.75.

Examples: Find the Equation through the given Points. 4. (3, -2) and (5, 0) The Equation of the line is y = x – 5.

Examples: Find the Equation through the given Points. 5. (8, -3) and (1, 4) The Equation of the line is y = -x + 5.

Let’s try Word Problems! Find Two Ordered Pairs Find the Equation Make sure to answer the question that is being asked!

Examples: The Equation of the line is y = .8x + 13. The cost of renting a car for the prom includes a flat rental fee plus a charge for each mile the car is driven. A car that is driven 105 miles costs $97. A car that is driven 115 miles costs $105. Find the equation that models the cost of renting a car. (105, 97) and (115, 105) The Equation of the line is y = .8x + 13.

Examples: The Equation of the line is y = -63.05x + 126869.50. In 1990, the price of a cell phone was $1400. In 2010, the price was $139. Find the equation that models the cost of cell phones. (1990, 1400) and (2010, 139) The Equation of the line is y = -63.05x + 126869.50.

Examples: y = 1.2x + 200 y = 1.2(12) + 200 y = 214.40 The cost of producing 4 units is $204.80. The cost of producing 8 units is $209.60. How much does it cost to produce 12 units? (4, 204.80) and (8, 209.60) y = 1.2x + 200 y = 1.2(12) + 200 y = 214.40

Examples: There were 174 words typed in 3 minutes. There were 348 words typed in 6 minutes. How many words will be typed in 8 minutes? (3, 174) and (6, 348) y = 58x + 0 y = 58(8) + 0 y = 464

Examples: y = 75x + 350 1100 = 75x + 350 750 = 75x 10 = x The attendance on the first day of a carnival was 425 people. The attendance on the third day was 575 people. On what day will there be 1100 people? (1, 425) and (3, 575) y = 75x + 350 1100 = 75x + 350 750 = 75x 10 = x

Examples: The cost of renting a van for the Senior-Week trip includes a flat rental fee plus a charge for each mile the car is driven. A car that is driven 325 miles costs $97. A car that is driven 405 miles costs $105. a. Find the equation of the line b. What is the flat rental fee? y, m, x, or b? c. What is the cost per mile? y, m, x, or b? d. How many miles can the seniors drive if they only have $600 to spend? y = .1x + 64.5 64.5 b .1 m y = .1x + 64.5 600 = .1x + 64.5 535.5 = .1x 5355 = x

Independent Practice

Exit Ticket