Graphing Linear Equations

Graphing and Systems of Equations Packet

Intro. To Graphing Linear Equations

The Coordinate Plane

A. The coordinate plane has 4 quadrants.

B. Each point in the coordinate plain has an x-coordinate (the abscissa) and a y-coordinate (the ordinate). The point is stated as an ordered pair (x,y).

C. Horizontal Axis is the X ? Axis. (y = 0)

D. Vertical Axis is the Y- Axis (x = 0)

Plot the following points:

a) (3,7)

b) (-4,5)

c) (-6,-1)

d) (6,-7)

e) (5,0)

f) (0,5)

g) (-5,0)

f) (0, -5)

y-axis

x-axis

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Graphing and Systems of Equations Packet

Slope Intercept Form

Before graphing linear equations, we need to be familiar with slope intercept form. To understand slope

intercept form, we need to understand two major terms: The slope and the y-intercept.

Slope (m):

The slope measures the steepness of a non-vertical line. It is sometimes referred to as the rise over run.

It's how fast and in what direction y changes compared to x.

y-intercept:

The y-intercept is where a line passes through the y axis. It is always stated as an ordered pair (x,y).

The x coordinate is always zero. The y coordinate can be found by plugging in 0 for the X in the equation or by finding exactly where the line crosses the y-axis. What are the coordinates of the y-intercept line pictured in the diagram above? : Some of you have worked with slope intercept form of a linear equation before. You may remember:

y = mx + b

Using y = mx + b, can you figure out the equation of the line pictured above?:

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Graphing and Systems of Equations Packet

Graphing Linear Equations

Graphing The Linear Equation: y = 3x - 5

1) Find the slope: m = 3 m = 3 . = y .

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x

2) Find the y-intercept: x = 0 , b = -5 (0, -5)

3) Plot the y-intercept

4) Use slope to find the next point: Start at (0,-5)

m = 3 . = y . up 3 on the y-axis

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x right 1 on the x-axis

(1,-2) Repeat: (2,1) (3,4) (4,7)

5) To plot to the left side of the y-axis, go to y-int. and

do the opposite. (Down 3 on the y, left 1 on the x)

(-1,-8)

6) Connect the dots.

1) y = 2x + 1

2) y = -4x + 5

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3) y = ? x ? 3

Graphing and Systems of Equations Packet

4) y= - x + 2

5) y = -x ? 3

6) y= 5x

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Graphing and Systems of Equations Packet

Q3 Quiz 3 Review

1) y = 4x - 6

2) y = -2x + 7

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