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Some warm-up problems first!!!. YAAAAAHHHHH!!!!. Graph y = 4. Horizontal Line. x. y. y = 4. 3 5 -3 2 -8. 4 4 4 4 4. In the coordinate plane, the graph of y = 4 is a horizontal line. y = # Horizontal Line. Graph x = 3. Vertical Line. x. y. x = 3. 3 3 3 3 3.
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Some warm-up problems first!!! YAAAAAHHHHH!!!!
Graph y = 4 Horizontal Line x y y = 4 • 3 • 5 • -3 • 2 • -8 4 4 4 4 4 In the coordinate plane, the graph of y = 4 is a horizontal line. y = # Horizontal Line
Graph x = 3 Vertical Line x y x = 3 • 3 • 3 • 3 • 3 • 3 -3 5 2 0 -8 In the coordinate plane, the graph of x = 3 is a vertical line. x = # Vertical Line
Graph 5x + 7y = 35 Solve for “y” 7y = -5x +35 7 7 7
Graph: y = 2x - 3 -2 -7 -1 -5 -3 0 1 -1
4.4 Graphing Using x and y Intercepts TODAY I AM GOING TO SHOW YOU AN EASIER WAY TO GRAPH LINES BUT REMEMBER WHEN ALL ELSE FAILS, YOU CAN ALWAYS SOLVE FOR Y AND MAKE A T-CHART!!!
The x-intercept of a graph is the point where the graph crosses the x-axis. • The y-intercept of a graph is the point where the graph crosses the y-axis.
y x - intercept X (2,0) (0,-1) y - intercept
Vocabulary – BIG CONCEPT x-intercept - the coordinate of a point where the graph crosses the x-axis. (Important – this is when y = 0) y-intercept - the coordinate of a point where the graph crosses the y-axis(when x = 0). y - intercept x - intercept
EXAMPLES OF X-INTERCEPTS (-2,0) (-1,0) (4,0) (0,0) (1.8,0) (-256,0) REMEMBER Y = 0 EXAMPLES OF Y-INTERCEPTS (0,5) (0,0) REMEMBER X = 0 (0,-44) (0,19)
Example 1: Find the x-intercept and the y-intercept of the graph of 3x - 4y = 12. • To find the x-intercept, plug zero in for y and solve for x. • To find the y-intercept, plug zero in for x and solve for y.
y-intercept 3x - 4y = 12 x-intercept 3x – 4(0) = 12 3x = 12 x = 4 • 3(0) – 4y= 12 • -4y = 12 • y = -3 (4,0) (0,-3) Make a small t-chart x y 4 0 0 -3
So when is it a good idea to use x and y intercepts to graph??? • When the two coefficients go into the constant!! • 2x + 3y = 6 • -3x – 4y = 24 • 12x + 5y = 60 • 5x – 4y = 40 These would not be a good idea to use x and y intercepts: 2x + 7y = 49 -3x + 6y = 7 5x – 9y = 13
Example 2: Graph the equation 4x + 8y = 24 using the x and y-intercepts. x-intercept y-intercept 4x + 8(0) = 24 4(0) + 8y = 24 4x = 24 8y = 24 (6,0) (0,3)
(0,3) 4x + 8y =24 (6,0)
Example 3: Identify the x-intercept and y-intercept of the graph. x-int: (2,0) y-int: (0,-4)
Graph 4x + 3y = 12 using intercepts Find x-intercept 4x + 3(0) = 12 Find y-intercept 4(0) + 3y = 12 4x = 12 3y = 12 x = 3 y = 4
Graph 3x + 5y = 15 using intercepts 5 DO YOU THINK THESE LINES INTERSECT???
Graph 2y = 3x - 6 using intercepts Put into Standard form first: Ax + By = C -3x + 2y = -6 2
Horizontal and Vertical Lines • The graph of y= # is HORIZONTAL • The graph x =# is VERTICAL
Graph 4y = 16 using 3-points • 4 • y = 4
Warm ups Find the x- and y- intercepts: • x – y = 4 • 2x + 3y = -6 • 3x + y = -5 • 4y = 2x – 12 • y = ½ x + 5 (4,0) (0,-4) (-3,0) (0,-2) (-5/3,0) (0,-5) (6,0) (0,-3) (-10,0) (0,5) -2x + 4y = -12 2y = x + 10 Get rid of fraction, multiply everything by 2 -x + 2y = 10
Graph in Standard Form: Steps: 1. Find the x- and y- intercepts 2. Graph x-intercept on x-axis ( ) 3. Graph y-intercept on y-axis ( ) 4. Connect the dots
Example 1 4x – 6y = 12 Y - intercept: 4(0) – 6y = 12 0 – 6y = 12 -6y = 12 y = -2 (0,-2) X – intercept: 4x – 6(0) = 12 4x – 0 = 12 4x = 12 x = 3 (3,0) Graph on y-axis Graph on x-axis
Example 2 2x + 4y = -6 Y - intercept: 2(0) + 4y = -6 0 + 4y = -6 4y = -6 y = -3/2 (0,-3/2) X – intercept: 2x + 4(0) = -6 2x – 0 = -6 2x = -6 x = -3 (-3,0)
Find the x and y intercepts of 4x + 3y = 12 To find the x - intercept: 1. Write the original equation. 4x + 3y= 12 2. 4x +3(0)= 12Substitute 0 for y 3. 4x = 12Solve for x The intercepts are at the points (3, 0) and (0,4) 4. x = 3Simplify • To find the y - intercept: • Write the original equation. 4x + 3y= 12 • 4(0) + 3y = 12 Substitute 0 for x • 3y = 12 Solve for y • y = 4 Simplify
Using intercepts, graph the line x – 2 = 4y Hint: Find the x and y intercepts – then connect the dots. Remember – 2 points determine a line!
TOO x – 6y = -6 y-intercept: (0,1) x-intercept: (-6,0) 6y = -3x + 18 y-intercept: (0,3) x-intercept: (6,0)
Quick Review • An x-intercept is the ______ coordinate of a point where a graph crosses the ____ axis. • At the x-intercept, the value of y is _____. • A y-intercept is the ______ coordinate of a point where a graph crosses the ____ axis. • At the y-intercept, the value of x is ______ . • To graph a line using the intercepts you need to……. • How many ways do you know how to graph NOW?
Example 4: You make and sell decorative bows. You sell small bows for $3 and large bows for $5. You want to earn $60 per week. This situation can be modeled by 3x + 5y = 60 where the x is the number of small bows and y is the number of large bows. a) Find the intercepts of the graph. b) Graph the equation. c) Give three possibilities for the number of each type of bow you can sell to earn $60.
y-intercept 3(0) + 5y = 60 5y = 60 y = 12 (0,12) 3x + 5y = 60 x-intercept 3x + 5(0) = 60 3x = 60 x = 20 (20,0)
(0,12) 3x + 5y = 60 (20,0)
3x + 5y = 60 3x + 5(9) = 60 3x + 45 = 60 3x = 15 x = 5 (5, 9) 3(10) + 5y = 60 30 + 5y = 60 5y = 30 y = 6 (10, 6) 3(15) + 5y = 60 45 + 5y = 60 5y = 15 y = 3 (15, 3) 1) 20 Small Bows , 0 Large Bows 2) 0 Small Bows, 12 Large Bows 3) 10 Small Bows, 6 Large Bows 4) 15 Small Bows, 3 Large Bows 5) 5 Small Bows, 9 Large Bows