Unit 5: Analytic Geometry

Determine the equation of this line:

Minds On

Unit 5: Analytic Geometry

• Determine the equation of your graph.

• Compare how your graph looks with how your partner’s graph looks

• Compare your equations

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

• Compare your Graphs

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

• Compare your equations

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

What can we conclude?

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Unit 5: Analytic Geometry

• Do you think this is always true? Why or why not?

• Lets find out! With your partner come up with 2 sets of equations with equal slopes and then we will graph them. Are they parallel?

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

• Determine the equation of your graph.

• Compare how your graph looks with how your partner’s graph looks

• Compare your equations

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

• Compare your graphs

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

• Compare your equations

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

What can we conclude?

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

• Do you think this is always true? Why or why not?

• Lets find out! With your partner come up with 2 sets of equations with slopes that are negative reciprocals and we will graph them. Are they perpendicular?

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

• A line is parallel to the line y = 3x -7. What could the equation of the line be? • How do you know?• Are there other possibilities?• Could the line go downward to

the right?

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

• Two lines are perpendicular. One has a y-intercept of 4 and the other has a y-intercept of -3. What could the equations be?

• How do you know?• Can both lines have positive slopes?• Can both lines have negative slopes?• Can either line have the positive

slope?

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

Let’s determine the slopes of these lines:

Do you see a pattern?

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

• What do you think the slope of this line is?

• Discuss with your partner.

• Think about how you would calculate it:

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

Horizontal lines have a slope of zero.

m = 0

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

Let’s determine the slope of these lines:

Do you see a pattern?

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

• What do you think the slope of this line is?

• Discuss with your partner.

• Think about how you would calculate it:

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Unit 5: Analytic Geometry

Vertical lines have a slope that is undefined.

m =

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Unit 5: Analytic Geometry

• Remember, the y-intercept is represented by b.

• And slope is represented by m.

• The equation of a line is y = mx + b

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Unit 5: Analytic Geometry

Determine the equation of this line:

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

What about horizontal

and vertical lines?

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

Determine the equation of this line:

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

Determine the equation of this line:

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

Find the equation of a line that is parallel to the line y = 2x – 4 and passes through the point (4, 1).

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

Determine the equation of a line with a slope of 0 and a y-intercept of 4.

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

Find the equation of a line that is perpendicular to the line y = -3x + 6 and passes through the point (-2, 5).

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

Find the equation of a line that does not have a y-intercept, but has an x-intercept of 7.

Lesson 7 – Special Cases

Unit 5: Analytic Geometry

Practice

Pg. 140 #2-10, 12, 13, 15

Lesson 7 – Special Cases