Study Unit 003 of MAT0511 - Analytic Geometry

1. Topic 1: Review
Study Unit 003: Analytic Geometry
Consider this table of values.
Does it represent a linear relationship?
What is the slope?
What is the y-intercept?
What is the equation?
Can you graph it?

2. Topic 1: Review
Study Unit 003 : Analytic Geometry
Use the table of values to graph the line.

3. Topic 1: Review
Study Unit 003 : Analytic Geometry
Learning Goals:
 I can find the slope between
two points using a graph
 I know the formula for
calculating the slope of a line
I can use the formula to find
the slope between two points.

4. Topic 1: Review
Study Unit 003 : Analytic Geometry
• The x-intercept is the point where
the line crosses the x-axis.
Its y-coordinate is 0.
• The y-intercept is the point where
the line crosses the y-axis.
Its x-coordinate is 0. The y-
intercept is represented by “b”

5. Study Unit 003 : Analytic Geometry
Remember all the different ways we can represent
slope.
m = slope
m =
m =
m =
m =
Rise: The vertical
distance between two
points
Run: The horizontal
distance between two
points
Topic 1: Review

6. Topic 1: Review
Study Unit 003 : Analytic Geometry
Remember that slope is a measure of the
steepness of a line.
As a line gets steeper its slope
As a line becomes more flat its slope
A line with a positive slope
A line with a negative slope

7. Topic 1: Review
Study Unit 003 : Analytic Geometry
Can you find the slope of this line?

8. Topic 1: Review
Study Unit 003 : Analytic Geometry
Find the slope of the line that passes through
the points (5, -2) and (3, 6)

9. Topic 1: Review
Study Unit 003 : Analytic Geometry
Find the slope of the line that has an x-intercept
of -5 and a y-intercept of 7.

10. Topic 1: Review
Study Unit 003 : Analytic Geometry
Learning Goals:
 I can write the equation of a
line given different pieces of
information about the line.

11. Topic 1: Review
Study Unit 003 : Analytic Geometry
The Equation of a Line is given by:
y = mx + b
where “m” is the slope and “b” is
the y-intercept.

12. Topic 1: Review
Study Unit 003 : Analytic Geometry
• Parallel lines have slopes that are the same.
• For example…. The line y = 3x – 6 is parallel to the line y =
3x + 1. I know because the slopes are the same.
• Perpendicular lines have slopes that are negative
reciprocals.
• For example…. The line y = 7x + 2 is perpendicular to the
line y = know because the slopes are negative reciprocals.
•

13. Topic 1: Review
Study Unit 003 : Analytic Geometry
• Horizontal lines have a slope of zero.
• Their equations look like y = #
• Vertical lines have a slope that is undefined.
• Their equations look like x = #

14. Topic 1: Review
Study Unit 003 : Analytic Geometry
Write the equation of a line that has a
slope of 7 and a y-intercept of 9.

15. Topic 1: Review
Study Unit 003 : Analytic Geometry
A line has an x-intercept of -3. and a slope
of 4. What is the equation of the line?

16. Topic 1: Review
Study Unit 003 : Analytic Geometry
Find the equation of the line that has a
slope that is undefined and goes through
the point (-4, -10).

17. Topic 1: Review
Study Unit 003 : Analytic Geometry
Find the equation of the line that is
passes through the point (2, -3) and is
parallel to the line y = -
•

18. Topic 1: Review
Study Unit 003 : Analytic Geometry
Find the equation of the line that passes
through the point (-2, 6) and is
perpendicular to y = 4x – 2.

19. Topic 1: Review
Study Unit 003 : Analytic Geometry
What is the equation of a line that has a
slope of zero and goes through the point
(6, -5)?

20. Topic 1: Review
Study Unit 003 : Analytic Geometry
Learning Goal
• I can interpret the meaning of slope and
y-intercept for a variety of word
problems.

21. Topic 1: Review
Study Unit 003 : Analytic Geometry
• Nico got a job wrapping presents over the holidays.
The equation P = x + 50 represents his pay where P
is his total pay per day and x is the number of
presents he wraps.
• What is the slope and what does it represent?
• What is the y-intercept and what does it
represent?

22. Topic 1: Review
Study Unit 003 : Analytic Geometry
• Nico got a job wrapping presents over the
holidays. The equation P = x + 50 represents his
pay where P is his total pay per day and x is the
number of presents he wraps.
c) How much would Nico get paid if he wrapped 300
presents?

23. Topic 1: Review
Study Unit 003 : Analytic Geometry
• Samantha purchased the original red ruby shoes worn
by Dorothy in the Wizard of Oz. As the shoes are a
collectible item they are expected to increase in value
as represented by the equation
V = 250,000 + 75t
where V is the value of the shoes and t is the number of
years since she purchased the shoes.
a) What is the slope and what does it represent?
b) What is the y-intercept and what does it represent?

24. Topic 1: Review
Study Unit 003 : Analytic Geometry
• Samantha purchased the original red ruby shoes worn
by Dorothy in the Wizard of Oz. As the shoes are a
collectible item they are expected to increase in value
as represented by the equation
V = 250,000 + 75t
where V is the value of the shoes and t is the number of
years since she purchased the shoes.
c) How much will the shoes be worth in 15 years?

25. Topic 1: Review
Study Unit 003 : Analytic Geometry
Learning Goal
 I can determine the rate of change of
segments of a time-distance graph.

26. Topic 1: Review
Study Unit 003 : Analytic Geometry
During which section
of the graph does
Rena travel the
fastest?
What do the negative
slopes represent?

27. Topic 1: Review
Study Unit 003 : Analytic Geometry