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)

Page 6 Answers[pic]

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Page 8 Answers

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[pic]

Name ____________________________________________________ Date _______________ Color________

Algebra I Ms. Hahl

Graphing Linear Equations

Directions: Graph the following linear equations on the coordinate plane provided.

1) [pic] 2) [pic]

3) [pic] 4) [pic]

5)[pic] 6) [pic]

7) [pic] 8) [pic]

9)[pic] 10) [pic]

11) [pic] 12) [pic]

ANSWERS

[pic]

[pic]

SLOPES

Name _________________________________________________ Date ___________ Color_________

Algebra I Ms. Hahl

Positive Negative

[pic] [pic]

[pic] [pic]

Zero Undefined

[pic] [pic]

[pic] [pic]

[pic] [pic]

Name _______________________________________________________ Date _____________ Color _________

Algebra I Ms. Hahl

Graphing Practice

Plot these points on the grid. Join them up in this order.

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Part I:

{1, 13} {3, 14} {6, 14} {7, 16} {8, 16} {7, 14} {11, 14} {13, 13} {13, 11} {13, 9} {13, 7} {12, 5}

{10, 3} {7, 3} {4,3} {2, 5} {1, 7} {1, 9} {1, 11} Join this last point up with {1, 13}.

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Part II:

{3, 9} {4, 11} {5, 9}. Join this last point up with {3, 9}.

*******************************************************************************

Part III:

{8,9} {9, 11} {10, 9}. Join this last point up with {8, 9}.

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Part IV:

{6, 8} {7, 8} {7,7} {6, 7}. Join this last point up with {6, 8}.

*******************************************************************************

Part V:

{4, 6} {6, 6} {6, 5} {7, 5} {7, 6} {8, 6} {8, 5} {9, 5} { 9, 6} {10, 6}

{9, 4} {8, 4} {7, 4} {6, 4} { 5, 4}. Join this last point up with {4, 6}.

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Name ________________________________________________ Date ___________ Color ________

Algebra I Ms. Hahl

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]

Name __________________________________________________________ Date __________ Color _______

Algebra I Ms. Hahl

Solving Systems of Equations Graphically

A system of equations is a collection of two or more equations with a same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system. When solving a system containing two linear equations there will be one ordered pair (x,y) that will work in both equations.

To solve such a system graphically, we will graph both lines on the same set of axis and look for the point of intersection. The point of intersection will be the one ordered pair that works in both equations. We must then CHECK the solution by substituting the x and y coordinates in BOTH ORIGINAL EQUATIONS.

Directions when solving Systems of Equations Graphically:

1) Put both lines into slope intercept form (y = mx + b)

2) Graph both lines on the same set of axis.

3) Find the point of intersection and label it. (This is the solution to the system.)

4) Make sure you label 5 THINGS!!! x-axis, y-axis, 1st line, 2nd line, and point of int.!!!!

5) Check your solution (point of intersection) in both original equations!!

Example: Solve the following system graphically, then check your solution.

[pic]

[pic]

::CHECK:: [pic]

1st equation: [pic]

[pic]

[pic]

[pic]

2nd equation: [pic]

[pic]

[pic]

[pic]

Do Now: Solve each of the systems of equations graphically, and then check your solution.

1) [pic]

[pic]

2)[pic]

[pic]

3) [pic]

[pic]

4) [pic]

[pic]

Directions: Solve each system graphically, and then graph your solution.

REMEMBER:

1) Put both lines into slope intercept form (y = mx + b)

2) Graph both lines on the same set of axis.

3) Find the point of intersection and label it. (This is the solution to the system.)

4) Make sure you label 5 THINGS!!! x-axis, y-axis, 1st line, 2nd line, and point of int.!!!!

5) Check your solution (point of intersection) in both original equations!!

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

[pic] [pic] [pic]

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

[pic] [pic] [pic]

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

[pic] [pic] [pic]

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

[pic] [pic] [pic]

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

[pic] [pic] [pic]

Page 4 Answers

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Extra Examples Answers

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