Graphing Linear Equations



Name _____________________________________________________ Date ____________ Color _________

Algebra I Ms. Hahl

Introduction to Graphing Linear Equations

The Coordinate Plane:

A – The coordinate plane has 4 quadrants.

B – Each point in the coordinate plane has an x coordinate (the abscissa) and the 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)

Directions: Plot the following points on the coordinate plane.

a) [pic] b) [pic] c) [pic] d) [pic]

e) [pic] f) [pic] g) [pic] h) [pic]

Graphing Linear Equations

To graph a line (linear equation), we first want to make sure the equation is in slope intercept form (y=mx+b). We will then use the slope and the y-intercept to graph the line.

Slope (m): Measures the steepness of a non-vertical line. It is sometimes refereed to as the rise/run or change in y/change in x. It’s how fast and in what direction y changes compared to x.

y-intercept(b): 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 taken from the “b” in y=mx+b.

Graphing The Linear Equation: [pic]

1) Find the slope: [pic] ( [pic] = [pic] = [pic]

2) Find the y-intercept: [pic] ( [pic]

3) Plot the y-intercept

4) Use slope to find the next point: Start at [pic]

[pic] ( up 3 on the y-axis

( right 1 on the x-axis

[pic] Repeat: [pic]

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)

[pic] Repeat:[pic]

6) Connect the dots.

Do Now: Graph the following linear equations.

1) [pic] 2) [pic]

3) [pic] 4) [pic]

5)[pic] 6) [pic]

7) [pic] 8) [pic]

Finding the Equation of a Linear Function

Finding the equation of a line in slope intercept form (y=mx + b)

Example: Find the equation in slope intercept form of the line formed by (3,8) and (-2, -7).

A. Find the slope (m): B. Use m and one point to find b:

[pic]  [pic]

[pic] Have: [pic]

[pic] [pic]

[pic] [pic]

[pic]

[pic]

[pic]

Special Slopes:

A. Zero Slope B. No Slope (undefined slope)

* No change in Y * No change in X

* Equation will be Y = * Equation will be X =

* Horizontal Line * Vertical Line

Practice Problems:

Find the equation in slope intercept form and then graph. (On some problems , the slope (m) is given, so you only have to find the y-intercept (b).)

1) [pic] 2) [pic]

3) [pic] 4) [pic]

5) [pic] 6) [pic]

7) [pic] 8) [pic]

Directions: Find the equation of each line in slope intercept form and then graph:

1) [pic] 2) [pic] 3) [pic]

4) [pic] 5) [pic] 6) [pic]

7) [pic] 8) [pic] 9) [pic]

10) [pic] 11) [pic] 12) [pic]

13) [pic] 14) [pic] 15) [pic]

16) [pic] 17) [pic]

Finding the Equation of a Parallel Line

Parallel Lines:

* Do not intersect

* Have same slopes

Example: Find for the given line, find a line that is parallel and

passes through the given point and then graph.

A) Given Line: [pic] Given Point: (12, 9)

[pic] [pic] [pic]

[pic]

[pic]

[pic]

[pic]

[pic]

Parallel Line: [pic]

Do Now: For the given line, find a line that is parallel and passes through the given point and then

graph both lines..

Given Line: Given Point:

1) [pic] (6,1)

2) [pic] [pic]

Given Line: Given Point:

3) [pic] [pic]

10) [pic] [pic]

Practice Problems: a) Use the two points to find the equation of the line.

b)      For the line found in part a, find a line that is parallel and passes through the given point.

c) Graph both lines.

Given Line: Parallel: Given Line: Parallel:

1) (-5, 13) (3, -3) (4,-10) 2) (-6,0) (3,6) (6,3)

3) (2,6)(-3,-19) (5,14) 4) (-4,3) (-8,6) (-4, 10)

5) (2,-5) (-2, -5) (8,-2) 6) (-9,-11)(6,9) (-3,-9)

7) (8,-3) (-4,9) (-2, 14) 8) (3,6)(3,-6) (11,-3)

9) (4,-3)(-6,-8) (6,7) 10) (2,4)(-6,-12) (-3,-5)

11) Find the equation of the line parallel to y = 3x – 2, passing through (-2, 1).

12) Find the equation of the line parallel to y = -¼ x + 2, passing through (-8, 7)

13) Find the equation of the line parallel to y = -5, passing through (2,7)

14) Find the equation of the line parallel to x= 8, passing through (4, -9)

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[pic]

[pic]

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