149 Views

Download Presentation
##### Today’s Agenda

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Today’s Agenda**• E - How can graphs be used to solve systems of linear equations? • A - Warm-up: Bell Ringer Patterns B • Review: Graph linear equations from slope-intercept form (graphic organizer) • T - New: System of Linear Equations (graphic organizer and video) • Class work: A Good Deal Shoulder Buddy Practice Problem • S – 3-2-1 Homework: Graphing Equations worksheet #1-6 Smyrna High School Geometry CP**Warm-up**Bell Ringer Day 1~Discovering Patterns… • Complete the pattern with your group. Then answer the questions as best you can. Smyrna High School Geometry CP**Pattern B**• Draw the penny pattern in figure 4. • How many pennies are in figure 5? • How many pennies are in figure 10? • What figure has 63 pennies? • Write a rule for this pattern? Smyrna High School Geometry CP**Unit 1 – Lesson 3: Systems of Linear Equations**Systems of Equations Two or more linear equations that have to be solved simultaneously. Smyrna High School Geometry CP**Check Skills You Will Need**How to Graph an Equation in Slope-Intercept Form y = mx + b • In the slope-intercept form of a linear equation, each letter represents a special value. • m = the slope of the equation (steepness). • b = the y-intercept (starting number). • With these two facts, an equation in slope-intercept form can be graphed. Smyrna High School Geometry CP**Check Skills You Will Need**How to Graph an Equation in Slope-Intercept Form y = mx + b • With these two facts, lets look at some examples. • y = 4x + 2 • First locate point b on the graph and mark it. Since this is the point where the graph of the equation crosses the y-axis, the x value will be zero and the y value will be b in the equation (0, b). Smyrna High School Geometry CP**Check Skills You Will Need**How to Graph an Equation in Slope-Intercept Form y = mx + b • Second, determine the slope (m) of the equation. • What number is before the x in the equation? • If there is not a number in front of the letter x, remember the number 1 is understood. Smyrna High School Geometry CP**Check Skills You Will Need**How to Graph an Equation in Slope-Intercept Form y = mx + b • Slope is commonly know as the rise/run. • The slope of the example can be written as 4/1. • Use these values to plot some more points. Smyrna High School Geometry CP**Check Skills You Will Need**How to Graph an Equation in Slope-Intercept Form y = mx + b • Start at the y-intercept (0, 2). • From this point use the slope of the equation to find a second point. • The slope of the line is 4/1 so count up 4 spaces (the rise) and count to the right 1 space (the run). • Repeat these steps to find a third point. Smyrna High School Geometry CP**Check Skills You Will Need**How to Graph an Equation in Slope-Intercept Form y = mx + b • Remember, the slope of the line will determine the direction of the rise and run. • Going up is a positive direction. Then run to the right. • Going down is a negative direction. Then run to the right. Smyrna High School Geometry CP**Check Skills You Will Need**How to Graph an Equation in Slope-Intercept Form y = mx + b • Remember, a negative divided by a negative is a positive. • Positive slopes will start lower on the left side of the graph and end up higher on the right side of the graph. • Negative slopes will start higher on the left side of the graph and end up lower on the right side of the graph. Smyrna High School Geometry CP**Pattern C**• How many toothpicks are in figure 5? • How many toothpicks are in figure 10? • What figure has 44 pennies? • Write a rule for this pattern. Smyrna High School Geometry CP**Check Skills You Will Need**How to Graph an Equation in Slope-Intercept Form y = mx + b • For practice, graph the following equations in slope-intercept form. • y = -x + 6 • y = 2x – 4 • y = ¼ x Smyrna High School Geometry CP**-1/1**(0, 6) 2/1 (0, - 4) (0, 0) 1/4 Smyrna High School Geometry CP**Graph!**• http://www.youtube.com/watch?v=2BHzXItkByU Smyrna High School Geometry CP**Ticket In The Door Recap**• For your equation do the following: • Circle & Identify the y-intercept (don’t forget to circle the sign also) • Graph the y-intercept (always on the y-axis) • Identify the slope (write it as a fraction) • Use slope to plot more points (ryse/run) • Draw a line through the points You may use your “yellow” graphic organizer to help guide you through the steps! Smyrna High School Geometry CP**Homework check**• Use the red pen to make corrections to your homework • Now, is NOT the time to do your homework • I should not see any writing utensils except the red pen • If you didn’t do your homework then you can turn it in tomorrow for half credit kuta graphing lines in slope intercept form hw.pdf Smyrna High School Geometry CP**Systems of Equations**• Let’s take a look at a few examples. • Your task: I Notice, I Wonder. • Discuss and write down some things that you notice about the examples. • Discuss and write down some things that you wonder about the examples. Smyrna High School Geometry CP**Systems of Equations: Example 1**Smyrna High School Geometry CP**Systems of Equations: Example 2**Smyrna High School Geometry CP**Systems of Equations: Example 3**Smyrna High School Geometry CP**Graphing Method**Substitution Method Elimination Method 3 Methods to Solve System of Equations Smyrna High School Geometry CP**1 Exact Solution**No Solution Infinitely Many Solutions 3 Possible Solution Types Smyrna High School Geometry CP**1 Exact Solution**Point of intersection Smyrna High School Geometry CP**Another type of solution**• How would you describe these lines? Y = 3x + 2 Y = 3x - 4 What do you think the solution (point of intersection) is? Smyrna High School Geometry CP**No Solution**Parallel Lines Will not intersect same slope different y-intercepts Smyrna High School Geometry CP**Another type of solution**• What do you notice about the graphs and equations? Y = -3x + 4 3x + y = 4 What do you think the solution (point of intersection) is? Smyrna High School Geometry CP**Infinitely Many Solutions**SAME LINE They are the SAME equation (just written in different forms) They have same slope and same y-intercept. Smyrna High School Geometry CP**The Goal of Solving Systems**• To find one pair (x, y) of values that satisfies both linear equations. • The one pair of values that makes both equations true. Smyrna High School Geometry CP**Hamilton High School**Smyrna High School Geometry CP**Hamilton High School**• Students in the Hamilton High School science club want to raise $240 to buy a special eyepiece for the high-powered telescope at their school. The PTA offered to pay club members for an after-school work project that would clean up a nearby park and recreation center building. • Because the outdoor work was harder and dirtier, the deal with the PTA would pay $20 for each outdoor worker ad $10 for each indoor worker. The club had 18 members eager to work on the project. Smyrna High School Geometry CP**Hamilton High School**• What do the variables x and y represent in these equations? • What problem condition is represented by the equation 20x+ 10y = 240? • What problem condition is represented by the equation x+ y = 18? • Determine 3 combinations of numbers of outdoor and indoor workers that will allow the club to earn just enough money to buy the telescope eyepiece? Smyrna High School Geometry CP**Think-Pair-ShareLet’s Look at the Solution**Complete Problem 1 - Parts a, b, c & d. Try it on your own Think: 5 minutes Check with a partner Pair: 2 minutes Whole group discussion Share: 5 minutes Smyrna High School Geometry CP**Hamilton High School**• What does the x represent? x: # of outdoor workers • What does the y represent? • y: # of indoor workers Smyrna High School Geometry CP**Hamilton High School**20x + 10y = 240 • What does this equation represent in the problem? • 20x + 10y = 240 shows the amount of money that can be earned depending on the # of outdoor and indoor workers Smyrna High School Geometry CP**Hamilton High School**x + y = 18 • What does this equation represent in the problem? • x + y = 18 shows that the # of club members who will work Smyrna High School Geometry CP**Let’s finish the problem**• Now, take a look at your 3 combination of workers from part d. • Will any of the combinations also put each willing club member to work? Smyrna High School Geometry CP**Today’s Agenda**• E - How can graphs be used to solve systems of linear equations? • A - Warm-up: Bell Ringer Patterns • Review: Graph linear equations from slope-intercept form (graphic organizer) • T - New: Graph linear equations from intercepts (graphic organizer) • Class work: A Good Deal Shoulder Buddy Practice Problem, Verifying solutions, Solving systems • S – Journal entry Homework: Pattern D Smyrna High School Geometry CP**WARMUP: Pattern E**• Draw the pattern for figure 5 • How many white tiles are in figure 5. • How many white tiles are in figure 8? • What figure has 72 white tiles. • Write a rule for the pattern. Smyrna High School Geometry CP**HOMEWORK: Pattern D**• How many toothpicks are in figure 5? • How many toothpicks are in figure 10? • What figure has 44 pennies? • Write a rule for this pattern. Smyrna High School Geometry CP**How Do We Graph a Linear Equation???**One way to graph a linear equation is in the form y = mx + b, where m is the slope and b is the y-intercept Smyrna High School Geometry CP**How Do We Graph a Linear Equation not in y=mx+b form???**Let’s Practice: -3x + 2y = 12 • Since it is not in y = mx + b, we will find the x- and y-intercepts and graph those points. • Find the x-intercept: Let y = 0 and solve the equation for x. • Find the y-intercept: Let x = 0 and solve the equation for y. Smyrna High School Geometry CP**How Do We Graph a Linear Equation???**Let’s Practice: -3x + 2y = 12 • Find the x-intercept: Let y = 0 and solve the equation for x. -3x + 2(0) = 12 -3x = 12 -3 -3 x = -4 or (-4, 0) Smyrna High School Geometry CP**How Do We Graph a Linear Equation???**Let’s Practice: -3x + 2y = 12 • Find the y-intercept: Let x = 0 and solve the equation for y. -3(0) + 2y= 12 2y= 12 2 2 y = 6 or (0, 6) Smyrna High School Geometry CP**How Do We Graph a Linear Equation???**You try… 6x - 4y = 12 Smyrna High School Geometry CP**Time to practice…**• Let’s do #5 & 6 together • Now it is your turn to finish the odd problems (1, 3, 7) Make sure that you have me check these problems (10 mins) • If you finish early, go ahead and finish the even problems (2, 4, 8). • If you don’t finish the evens in class, you can finish them for homework. graphing lines using intercepts.pdf Smyrna High School Geometry CP**How Do We Graph a Linear Equation???**Let’s Practice with Hamilton High: 20x + 10y = 240 • Find the x-intercept: Let y = 0 and solve the equation for x. • 20x + 10(0) = 240 • 20x = 240 • 20 • x = 12 or (12, 0) Smyrna High School Geometry CP**How Do We Graph a Linear Equation???**Let’s Practice: 20x + 10y = 240 • Find the y-intercept: Let x = 0 and solve the equation for y. • 20(0) + 10y= 240 • 10x = 240 • 10 10 • y = 24 or (0, 24) Smyrna High School Geometry CP