notes chapter 3 section 5 graph a line using intercepts essential question why are graphs helpful?...
TRANSCRIPT
Notes Chapter 3 Section 5 Graph a Line Using Intercepts
Essential Question WHY are graphs helpful?
Vocabulary: x-intercept & y-interceptCommon Core State Standards: 8.EE.8c
Page 209
• What you will learn • Take a minute to scan the lesson and predict
two things you will learn about the intercepts.
• 1. the x-intercept is the x-coordinate of the point where the graph crosses the x-axis
• 2. You can use the x- and y-intercepts to graph a linear equation.
Page 209
• Real-World Link • Launch the Lesson - Movie• http://connected.mcgraw-hill.com/c2j/syllabu
s.syllabusLesson.do?bookId=WMVDSJSEQ6HGKX6J8K6Q6SLQK1&lessonId=2CP14BWC792NM4XM63G2PP7HCQ
Page 209
• Real-World Link -Mrs. Hodges spent $80 on movie tickets and drinks for her son and his friends. The total cost of x movie tickets and y drinks is represented by the equation
• 8x + 4y = 80.
• 1. Write in slope intercept form
Item CostTickets $8
Drinks $4
Page 209
• Real-World Link• 1. Write in slope intercept form• 8x + 4y = 80.• -8x -8x• 4y = -8x + 80• 4 4• y = -2x + 20
Page 209
• Real-World Link• y = -2x + 20• 2. Graph the equation
Page 209
• Real-World Link• 3. What does the point (0,20) represent? • y = -2x + 20
0 2 4 6 8 10 120
5
10
15
20
25
Y-axis drinks
X-axistickets
Page 210
• The y-intercept of a line is the y-coordinate of the point where the graph crosses the y axis.
• The x-intercept of a line is the x-coordinate of the point where the graph crosses the x-axis.
Visual 1
Visual 2
Visual 3
Page 210
• State the x- and y-intercepts of y = 1.5x -9. Then use the intercepts to graph the equation.
• The equation is in slope-intercept form so the y-intercept is -9 or the point (0,-9)
• To find the x-intercept, let y=0 and solve for x.• 0 = 1.5x – 9• +9 + 9 add 9 to both sides of the equation• 9 = 1.5x divide both sides of the equation by 1.5• 1.5 1.5• 6 = x the x-intercept is 6 or the point (6,0)
Page 210
• y-intercept is -9 or the point (0,-9)• the x-intercept is 6 or the point (6,0)
0 1 2 3 4 5 6 7
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
Page 210 – Got It a and b
• You have 3 minutes to complete Got it problem a Get going!!
• y = (-1/3)x + 5 y-intercept is 5 the point (0,5)• Let y =0 and solve for x• 0 = (-1/3)x + 5• -5 - 5 subtract 5 from both sides of the equation
• -5 = (-1/3)x• (-3/1)*-5 = (-3/1)*(-1/3)x multiply both sides of the equation by -3
• 15 = x x-intercept is 15 the point (15,0)
Page 210 – Got It a and b
• You have 3 minutes to complete Got it problem b Get going!!
• y = (-3/2)x + 3 y-intercept is 3 the point (0,3)• Let y =0 and solve for x• 0 = (-3/2)x + 3• -3 - 3 subtract 3 from both sides of the equation
• -3 = (-3/2)x• (-2/3)*-3=(-2/3)*(-3/2)x multiply both sides of the equation by -2/3
• 2 = x x-intercept is 2 the point (2,0)
Page 211
• Mauldin Middle School wants to make $4,740 from yearbooks. Print yearbooks x cost $60 and digital yearbooks y cost $15. This can be represented by the equation 60x+15y=$4,740.
• Use the x- and y-intercepts to graph the equation.
Page 211
• Use the x- and y-intercepts to graph the equation.
X-intercept Y-intercept
60x + 16y = 4,74060x + 16(0) = 4,74060x = 4,740 divide by 60X=79
60x + 16y = 4,74060(0) + 16y = 4,74016y = 4,740 divide by 16Y=316
Page 211
• Use the x- and y-intercepts to graph the equation. X-intercept Y-intercept
X=79 Y=316
0 10 20 30 40 50 60 70 80 900
50
100
150
200
250
300
350
Page 211 – Got It c
• You have 3 minutes to complete Got it problem c Get going!!
• Mr. Davies spent $230 on lunch for his class. Sandwiches x cost $6 and drinks y cost $2. This can be represented by the equation 6x+2y=230. Use the x- and y-intercepts to graph the equation. Then interpret the intercepts.
Page 211 – Got It c
• 6x+2y=230X intercept (sandwiches) let y=0
Y intercept (drinks) let x=0
6x+2y=2306x+2(0)=2306x = 230X=230/6X=38.33
6x+2y=2306(0)+2y=2302y=230Y=115
0 5 10 15 20 25 30 35 40 450
20
40
60
80
100
120
140
38.33 sandwiches & 0 drinks = $230 and
0 sandwiches & 115 drinks = $230
Page 212
• Guided Practice• I will work the odd• You will work the even
Page 212
• Guided Practice• 1. y = 3x – 9 y intercept is -9• 0 = 3x – 9 let y = 0• 9 = 3x add 9 to both
sides• 3 = x divide both sides
by 3 x intercept is 3
Page 212
• Guided Practice• 1. y = 3x – 9 ; y intercept is -9, x intercept is 3
Page 212
• Guided Practice• 3. 6x + 8y = 288
X intercept Y intercept
6x + 8y = 2886x + 8(0) = 2886x = 288X=48
6x + 8y = 2886(0) + 8y = 2888y = 288Y=36
Page 212
• Guided Practice• 3. 6x + 8y = 288
X intercept Y intercept
X=48 Y=36
Page 212
• Guided Practice You do the even
Page 212
• Guided Practice• 2) x-intercept = -4; y-intercept=2
• 4) how many points are needed to graph a line? The intercepts give you 2 points.
Homework 3.5
• Independent Practice• Pages 213-214 problems 1-9
Quick Review
Graph
Linear Equationy = 3x – 2
Y-intercept
is -2
X-intercept is 2/3