From yesterday in case you didn’t get it Horizontal Line x y y = 4 3 5 -3 2 -8 4 In the coordinate plane, the graph of y = 4 is a horizontal line. y = # Horizontal Line

From yesterday in case you didn’t get it Vertical Line x y x = 3 3 -3 5 2 -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 X -values Y- values 7 7 7 X -values Y= -5/7x +5 Y- values (X, Y) -7 -5/7(-7)+5 10 (-7, 10) -5/7(0)+5 5 (0,5) 7 -5/7(7)+5 (7, 0)

Find 3 points using the table, and graph the line of the equation Find 3 points using the table, and graph the line of the equation. y = 2x - 3 -2 -7 -1 -5 -3 1 -1 This is a review, scaffolding slide. Have each student graph the equation at their desk. W#alk around and check.

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 x - intercept y - intercept (2,0) (0,-1) Definitions. Instruct student to add to notebook. 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.

(4,0) (0,-3) y-intercept 3(0) – 4y= 12 -4y = 12 y = -3 3x - 4y = 12 x-intercept 3x – 4(0) = 12 3x = 12 x = 4 y-intercept 3(0) – 4y= 12 -4y = 12 y = -3 (4,0) (0,-3) Make a small t-chart x y 4 -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

Example 2: Graph the equation 4x + 8y =24 using the x and y-intercepts. Find the x and y-intercepts. Plot the x and y-intercepts and draw a line through them connecting them with a straight edge. 4x + 8y =24 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 Teach and demonstrate the concept.

Graph 2x + 3y = 12 using intercepts 6 This slide introduces the X-Y intercept table. Teach and demonstrate the steps.

Graph 3x + 5y = 15 using intercepts 5 Have students make an intercept table and graph the equation on each of the next 6 slides. The steps are shown for students still needing to see it. I provide graph paper with 6 graphs per front and back. DO YOU THINK THESE LINES INTERSECT???

Graph 5x - 2y = 10 using intercepts 2

Graph 2y = 3x - 6 using intercepts Put into Standard form first: Ax + By = C -3x + 2y = -6 x y 2 This is the first problem not in slope intercept form and will catch many. Teach.

Horizontal and Vertical Lines The graph of y= # is HORIZONTAL The graph x =# is VERTICAL

Graph 4y = 16 using 3-points 4 y = 4 x y 3 6

Graph 3x = 18 using 3-points x = 6 x y 3 - 4

Warm ups Find the x- and y- intercepts: x – y = 4 2x + 3y = -6 (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 (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 (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) = 12 Substitute 0 for y 3. 4x = 12 Solve for x The intercepts are at the points (3, 0) and (0,4) 4. x = 3 Simplify 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!

Using intercepts, graph the line y = -2x + 25

Graph the equation: 2x + 5y = 10

TOO x – 6y = -6 6y = -3x + 18 y-intercept: (0,1) 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 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.

3x + 5y = 60 x-intercept 3x + 5(0) = 60 3x = 60 x = 20 (20,0) y-intercept 3(0) + 5y = 60 5y = 60 y = 12 (0,12)

(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