3.1 The Rectangular Coordinate System.notebook
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3.1 The Rectangular Coordinate System
Objectives• Interpret a line graph• Plot ordered pairs• Find ordered pairs that satisfy a given equation• Graph lines• Find x- intercepts and y-intercepts• Use the Midpoint formula
3.1 The Rectangular Coordinate System.notebook
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Interpret a Line GraphThe graph indicates US federal government tax revenues in billions of dollars (a) If the ordered pair (x,y)
represents a point on the graph, what does x represent? What does y represent?
(b) Estimate revenue in 2002.
(c) Write an ordered pair (x,y) that approximates federal revenue in 2002.
(d) What does the ordered pair (2000, 2030) mean in context of this graph.
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x
y
Origin (0,0)III
IVIII
The Coordinate Plane a.k.a. rectangular coordinate system
Ordered pair (x,y)
Is the ordered pair (6, 2) a solution to the equation 2x+3y=6? Justify your answer.
Is (9, -3)? Justify.
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Graph the linear equation by creating a table of values. y = 2x1.
x
yx y
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Standard Form of a Linear EquationAx + By = C
where A, B & C are real #s (A and B both ≠ 0)
xintercept: point where graph intersects the xaxis
yintercept: point where graph intersects the yaxis
These equations are in standard form:
5x + 2y = 10 x + 4y = 8 6x 3y = 6
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Graphing Linear Equations by Intercept Method
1st Find the xintercept by substituting 0 in for y. Solve for x. 2nd Find yintercept by substituting 0 in for x. Solve for y.3rd Draw a line through the two points you found in steps 1 & 2.4th Label the line.
Graph by intercept method.
1. 2x + 6y = 18
2. x - 4y = 8
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Graph by intercept methody - 3x=9 x + y = 53. 4.
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Midpoint
Sometimes you need to find the point that is exactly between two other points. If you need to find the point that is exactly halfway between two given points, just average the xvalues and the yvalues.
Here is the formula:
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Find the midpoint between (–1, 2) and (3, –6) Use of the graph is optional...
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Find the midpoint between (5, 4) and (6, 2) Use of the graph is optional...
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Click here for link
Worksheet with graphing by intercept method and finding midpoint
Practice
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Homework p. 115-116#2, 9, 23,2537-49 odd55, 57
Attachments
Slope and graphing practice for chapter 3.docx
Graphing by intercept method and midpoint practice.docx
Name_________________________________
Graphing Linear Equations
Recall the slope formula:
1. Find the slope of the line that passes through the given points.
(Use of the graph is optional)
a) (-2, 7) and (-5, 1)b) (5, 8) and (6, -1)
c) (-1, 2) and (-1, 5)d) (2, 4) and (0, 4)
2. Graph each of the following linear equations. Show work.
a) y = 4x+1b)
c) 3y +6x = 9d) 7x-2y = 14 Try using intercept method!
3. Graph each on the axes below. LABEL!!
a) x = -2 b) y = 5
SMART Notebook
Name________________________________
Math 12
Graphing by Intercept Method
1. Graph each of the following by intercept method. Label each line.
a) b) c)
SMART Notebook
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