Algebra 1 2.2.1

Bellringer Mallory had $1 this morning and asked her mom for another. Instead of giving Mallory more money, her mom said she would give Mallory $2 the next day if she still had the dollar she was holding. Plus, she would continue to give Mallory $2 each day as long as she saved it all. Mallory agreed to the deal and began to wonder how much money she might have at the end of the week. To find out, Mallory graphed the equation y = 2x + 1, shown, where x represents the number of days and y represents the amount of money she would have. Dollars Days

Bellringer If today, Day 0, is Monday and x is in days, how much could Mallory have on Wednesday? How much could Mallory have on Friday? How does the graph represent Mallory’s mother giving her $2 each day? Dollars Days

Bellringer-debrief If today, Day 0, is Monday and x is in days, how much could Mallory have on Wednesday? If Monday is 0, Wednesday is 2. Substitute this value into the equation Mallory used. y = 2x + 1 Equation y = 2(2) + 1 = $5 Substitute 2 for x. Mallory could have $5 on Wednesday.

Bellringer-debrief How much could Mallory have on Friday? Friday is Day 4 on the graph. Substitute this value into the equation. y = 2x + 1 Equation y = 2(4) + 1 = $9 Substitute 4 for x. Mallory could have $9 on Friday.

Bellringer-debrief How does the graph represent Mallory’s mother giving her $2 each day? The slope of the graph is 2. The graph shows that Mallory can receive $2 on the y-axis for every 1 day on the x-axis.

Standard Standard:

Learning TargetS I will be graphing equations with two variables. I will be asked to read points from a graph. I will be asked to take values of x to find values for y.

Mini Lesson Key Concepts A solution to an equation with two variables is an ordered pair, written (x, y). Ordered pairs can be plotted in the coordinate plane. The path the plotted ordered pairs describe is called a curve. A curve may be without curvature, and therefore is a line.

Mini Lesson Key Concepts, continued An equation whose graph is a line is a linear equation. The solution set of an equation is infinite. When we graph the solution set of an equation, we connect the plotted ordered pairs with a curve that represents the complete solution set.

Work Session Guided Practice Example Graph the solution set for the equation y = 3x.

Work Session Guided Practice: Example, continued Make a table. x y –2 Choose at least 3 values for x and find the corresponding values of y using the equation. x y –2 –1 1 3 2 9

Work Session Guided Practice: Example continued Plot the ordered pairs in the coordinate plane.

Work Session Guided Practice: Example, continued Notice the points do not fall on a line. The solution set for y = 3x is an exponential curve. Connect the points by drawing a curve through them. Use arrows at each end of the line to demonstrate that the curve continues indefinitely in each direction. This represents all of the solutions for the equation.

Work Session Guided Practice Example 2 The Russell family is driving 1,000 miles to the beach for vacation. They are driving at an average rate of 60 miles per hour. Write an equation that represents the distance remaining in miles and the time in hours they have been driving, until they reach the beach. They plan on stopping 4 times during the trip. Draw a graph that represents all of the possible distances and times they could stop on their drive.

Work Session Guided Practice: Example 2, continued Write an equation to represent the distance from the beach. Let d = 1000 – 60t, where d is the distance remaining in miles and t is the time in hours.

Work Session Guided Practice: Example 2, continued Make a table. Choose values for t and find the corresponding values of d. The trip begins at time 0. Let 0 = the first value of t. The problem states that the Russells plan to stop 4 times on their trip. Choose 4 additional values for t. Let’s use 2, 5, 10, and 15. Use the equation d = 1000 – 60t to find d for each value of t. Fill in the table.

Work Session Guided Practice: Example 2, continued t d 1000 2 880 5 1000 2 880 5 700 10 400 15 100

Distance remaining in miles Work Session Guided Practice: Example 2, continued Plot the ordered pairs on a coordinate plane. Distance remaining in miles Time in hours

Distance remaining in miles Work Session Guided Practice: Example 2, continued Connect the points by drawing a line. Do not use arrows at each end of the line because the line does not continue in each direction. This represents all of the possible stopping points in distance and time. Distance remaining in miles Time in hours

Closing Find three solutions that will satisfy the equation

Homework 2.2.1 Page ________ #3, 4, 8, 9, 10