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**Graphs & Linear Equations**

Y y=mx+b X

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**A Point (X,Y) (4,3) • (X,Y) is called an Ordered Pair Y X**

The X value or X Coordinate is the location of a point in the X direction The Y value or Y Coordinate is the location of a point in the Y direction

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**How to Graph a Point Y (X,Y) (4,2) • 321 X -4-3-2-1 0 1 2 3 4**

X is the distance along the x=axis Y is the distance along the y=axis Y 3210 HINT: Think of the x-axis as the Number Line X -1 -2 HINT: Think of the y-axis a vertical Number Line

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**Important Vocabulary for Graphs**

The Graph itself is called the x-y plane (ie. Plane surface) or The Coordinate Plane or Cartesian Coordinate Plane after Renee Descartes Y y-axis 2nd Quadrant 1st Quadrant (+X,+Y) (-X,+Y) X x-axis (-X,-Y) (+X,-Y) 3rd Quadrant 4th Quadrant Quadrants start with Positive X & Y and go Counter Clockwise

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**Graphing Linear Equations (Find 3 Domain & Range Points)**

First Degree Equations are Lines (y=mx+b) and you calculate 3 (X,Y) values Make sure the points line up on a x-y graph and connect the dots.

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**RECALL X-Domain & Y-Range**

Graphing Lines is just like finding the Range of 3 Domain Points: (Substitute each Domain value into the equation) y = 2x-7 when the Domain is {-2, 0, 2} f(-2) = 2•(-2) -7 = = (-2,-11) f(0) = 2•(0) -7 = 0 -7 = (0,-7) f(2) = 2•(2) -7 = 4 -7 = (2,-3) Answer: RANGE: {-11, -7, -3}

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**Practice Finding 3 Points Given a Linear Equation**

Find any 3 (X,Y) points for the following equations: y=5x y=4x-5 y=3x+1 (Hint: Try x=0)

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Sample Solutions x y = 5x 0 0 5 10 x y = 4x-5 x y = 3x+1

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Now Graph the 3 Points x y = 5x 0 0 5 10 • (2,10) • (1,5) • (0,0)

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**What is Intercept in Math?**

Y X An Intercept is the coordinate where a line crosses the x or y axis

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**Using X&Y Intercepts to Graph a Line**

y-axis The Y intercept is the y coordinate (where a line crosses the y axis). • (0,2) • (3,0) X x-axis The X intercept is the x coordinate (where a line crosses the x axis).

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**Name the X&Y Intercepts**

y-axis • (0,2) • (3,0) X x-axis

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**Name the X&Y Intercepts**

y-axis • (0,2) • X x-axis (-2,0)

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**Name the X&Y Intercepts**

y-axis X x-axis

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**Name the X&Y Intercepts**

y-axis X x-axis

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**What is the value of x at the y intercept**

What is the value of x at the y intercept? What is the value of Y at the x-intercept? Y y-axis X x-axis

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**Find the x- and y-intercepts. 1. x - 2y = 12**

x-intercept: Plug in 0 for y. x - 2(0) = 12 x = 12; (12, 0) y-intercept: Plug in 0 for x. 0 - 2y = 12 y = -6; (0, -6)

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**Find the x- and y-intercepts. 2. -3x + 5y = 9**

x-intercept: Plug in 0 for y. -3x - 5(0) = 9 -3x = 9 x = -3; (-3, 0) y-intercept: Plug in 0 for x. -3(0) + 5y = 9 5y = 9 y = ; (0, )

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**What is the x-intercept of 3x – 4y = 24?**

(3, 0) (8, 0) (0, -4) (0, -6) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

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**What is the y-intercept of -x + 2y = 8?**

(-1, 0) (-8, 0) (0, 2) (0, 4) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

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**Graph y = 2x - 6 using x&y intercepts**

Graph Linear Eq. Graph y = 2x - 6 using x&y intercepts X Y = 2x - 6 1st Make x-y table Y y-axis X x-axis

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**Graph y = 2x - 6 using x&y intercepts**

Graph Linear Eq. Graph y = 2x - 6 using x&y intercepts X Y = 2x - 6 0 -6 1st Make x-y table 2nd Set x = 0 and solve for y Y y-axis X x-axis • (0,-6)

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**Graph y = 2x - 6 using x&y intercepts**

Graph Linear Eq. Graph y = 2x - 6 using x&y intercepts X Y = 2x - 6 0 -6 1st Make x-y table 2nd Set x = 0 and solve for y 3rd Set y = 0 and solve for x Y y-axis • (3,0) X x-axis • (0,-6)

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**Graph y = 2x - 6 using x&y intercepts**

Graph Linear Eq. Graph y = 2x - 6 using x&y intercepts X Y = 2x - 6 0 -6 1st Make x-y table 2nd Set x = 0 and solve for y 3rd Set y = 0 and solve for x 4th Plot these 2 points and draw line Y y-axis • (3,0) X x-axis • (0,-6)

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**Graph y = 2x - 6 using x&y intercepts**

Graph Linear Eq. Graph y = 2x - 6 using x&y intercepts X Y = 2x - 6 0 -6 4 2 1st Make x-y table 2nd Set x = 0 and solve for y 3rd Set y = 0 and solve for x 4th Plot these 2 points and draw line 5th Use 3rd point to check Y y-axis • (4,2) • (3,0) X x-axis • (0,-6)

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**Graphing Horizontal & Vertical Lines**

This line has a y value of 4 for any x-value. It’s equation is y = 4 (meaning y always equals 4) Y y-axis X x-axis

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**Graphing Horizontal & Vertical Lines**

This line has a x value of 1 for any y-value. It’s equation is x = 1 (meaning x always equals 1) Y y-axis X x-axis

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**The Equation of a Vertical Line is X=Constant**

Y y-axis x = 1 X x-axis

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**The Equation of a Horizontal Line is Y=Constant**

y-axis y = 3 X x-axis

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**Graph the following lines**

Y = -4 Y = 2 X = 5 X = -5 X = 0 Y = 0

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Answers x = -5 x = 5 Y y-axis X x-axis

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Answers Y y-axis y = 2 X x-axis y = -4

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Answers Y y-axis y = 0 X x-axis x = 0

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Unit 1 Solving Linear Systems by Graphing

Unit 1 Solving Linear Systems by Graphing

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