M9 Exercise A

1. Find the coordinates of the point plotted below

12345-1-2-3-4-512345-1-2-3-4-5

Coordinates: ( ,

2. To use this drawing tool, click on the graph at two different points to position the line.

Graph the equation of the line x=1x=1.

3. Fill out the chart below, then plot each point on the grid.

y=x−3y=x-3
x y
0
1
2
3

4. To use this drawing tool, click on the graph at two different points to position the line.

Graph the equation of the line y=−1y=-1.

5. Fill in the t-table below for the equation. Then graph the line on the grid by selecting two of the points from your table.

−3x+4y=−8-3x+4y=-8

x y
−4-4

0

4

12345678-1-2-3-4-5-6-7-812345678-1-2-3-4-5-6-7-8
Clear All Draw:

6. In which quadrant does the point (2,2)(2,2) lie?

• IV
• II
• I
• III

7. Sketch a graph of x+2y=−4x+2y=-4
12345-1-2-3-4-512345-1-2-3-4-5
Clear All Draw:

8. Plot the point (2,2)(2,2).
12345-1-2-3-4-512345-1-2-3-4-5
Clear All Draw:

M9 Practice B

1. Given a line passing through (−5,4)(-5,4) and (−7,12)(-7,12), a) which of the following is the correct slope of the line AND b) what is the slope?
• m=(12)−(4)(−7)−(5)m=(12)-(4)(-7)-(5)
• m=(−7)−(−5)(12)−(4)m=(-7)-(-5)(12)-(4)
• m=(12)−(4)(−7)−(−5)m=(12)-(4)(-7)-(-5)
• m=(−7)−(−5)(12)−(−4)m=(-7)-(-5)(12)-(-4)
slope =

2. 14-10

State the run, rise, and slope of the line above.

3. Find the slope of the line that goes through the points (14,6) and (15,2).

Slope, mm =

Enter your answer as an integer or a reduced fraction in the form A/B

4. Determine the slope of the line passing through the points (9,2)(9,2) and (−3,−4)(-3,-4).

m=m=

5. 1020304050-10-20-30-40-5048121620-4-8-12-16-20

Find the slope of the line.

Slope = m=m=

Enter your answer as an integer or as a reduced fraction in the form A/B.

6. Match each slope with the type of line it will produce.
Slope
• -1
• 0
• DNE
Type of Line
a. uphill
b. Horizontal
c. Vertical
d. Downhill

7. Find the slope of the line shown below
123-1-2-312345-1-2-3-4-5
slope =

8. Find the slope between the points (−4,4)(-4,4) and (−2,4)(-2,4). Enter DNE if the slope between the points is undefined.
Slope:

9. A city's population in the year x=x=1970 was y=y= 911,800. In 1988 the population was 913,600.

Compute the slope of the population growth (or decline) and choose the most accurate statement from the following:
• The population is increasing at a rate of 50 people per year.
• The population is increasing at a rate of 100 people per year.
• The population is decreasing at a rate of 100 people per year.
• The population is increasing at a rate of 300 people per year.
• The population is decreasing at a rate of 50 people per year.
• The population is decreasing at a rate of 300 people per year.

10. Sketch a line with positive slope and positive y-intercept.

12345-1-2-3-4-512345-1-2-3-4-5
Clear All Draw:

Practice Exercise C

Question 1
The equation of the line with slope 2 and y-intercept 3 can be written in the form y=mx+by=mx+b where
the number mm is:
the number bb is:

Question 2 Graph




Graph the following equation. y=−3x+1y=-3x+1
Clear All Draw:

Question 3 Graph





Graph the following equation. y=−x+4y=-x+4
Clear All Draw:

Question 4

Determine whether the given points are on the graph of y=−2x+5y=-2x+5.

Select all points that lie on the graph.
• (-2,9)
• (3,-1)
• (-1,3)
• (2,-6)

Question 5


Give the slope and the y-intercept of the line y=x−3y=x-3.
Make sure the y-intercept is written as a coordinate.

Slope =

y-intercept =

Question 6
Graph the following equation. y=2x−1y=2x-1

Question 7
Graph the equation −2x+4y=−20-2x+4y=-20 by writing the equation in the form y=mx+by=mx+b.
Clear All Draw:

Question 8
Graph the equation 4x−5y=154x-5y=15 by writing the equation in slope-intercept form.
Clear All Draw:

Question 9
Graph the following equation. y=x−8y=x-8
Clear All Draw:

Question 10
Which of these is the slope-intercept form of a linear equation?
• xy=m+b
• x=my+b
• ax+by=c
• y=mx+b
• None of these

M9 Problem Set
Question 1
In which quadrant does the point (6,−4)(6,-4) lie?

• IV
• I
• II
• III

Question 2
Plot these points:

x y
8 7
1 4
6 2
5 3
3 8
Clear All Draw:

3. Find the coordinates of the point plotted below

12345-1-2-3-4-512345-1-2-3-4-5

Coordinates: ( , )

4. For the equation 3x+4y=123x+4y=12

a) Complete the table:
x y

0
0

b) Plot the two points you found in the table.
123456-1-2-3-4-5-6123456-1-2-3-4-5-6
Clear All Draw: Dot

5. Fill in the t-table below for the equation. Then graph the line on the grid by selecting two of the points from your table.

y=−2x−6y=-2x-6

x y
-1

0

1

12345678910-1-2-3-4-5-6-7-8-9-1012345678910-1-2-3-4-5-6-7-8-9-10
Clear All Draw:

6. Sketch a graph of x−y=−4x-y=-4
12345-1-2-3-4-512345-1-2-3-4-5
Clear All Draw:

7. To use this drawing tool, click on the graph at two different points to position the line.

Graph the equation of the line y=2y=2.

12345-1-2-3-4-512345-1-2-3-4-5
Clear All Draw:

8. What kind of slope does this line have?

9. 3 -13
State the run, rise, and slope of the line above.

run =

rise =

m =

10. Given a line passing through (−6,9)(-6,9) and (6,19)(6,19), a) which of the following is the correct slope of the line AND b) what is the slope?
• m=(6)−(−6)(19)−(9)m=(6)-(-6)(19)-(9)
• m=(6)−(−6)(19)−(−9)m=(6)-(-6)(19)-(-9)
• m=(19)−(9)(6)−(−6)m=(19)-(9)(6)-(-6)
• m=(19)−(9)(6)−(6)m=(19)-(9)(6)-(6)
slope =

11. Sketch a line with positive slope and negative y-intercept.

12. Find the slope between the points (13,7) and (12,9).

Slope =

13. Find the slope between the points (−10,−5)(-10,-5) and (10,−5)(10,-5). Enter DNE if the slope between the points is undefined.
Slope:

14. Find the slope of the line that goes through the points (3,4) and (12,15).

Slope, mm =

Enter your answer as an integer or a reduced fraction in the form A/B

15. (See the graft)
Find the slope of the line.

Slope = m=m=

Enter your answer as an integer or as a reduced fraction in the form A/B.

16. (See the graft)
Find the slope of the line.

Slope = m=m=

17. A city's population in the year x=x=1955 was y=y= 1,733,150. In 1950 the population was 1,734,400.

Compute the slope of the population growth (or decline) and choose the most accurate statement from the following:
• The population is increasing at a rate of 250 people per year.
• The population is decreasing at a rate of 400 people per year.
• The population is decreasing at a rate of 450 people per year.
• The population is decreasing at a rate of 250 people per year.
• The population is increasing at a rate of 450 people per year.
• The population is increasing at a rate of 400 people per year.

18. At 11 AM, one share of Starbucks stock was $15. By 1 PM the price was $21.

The rate the Starbucks stock value was changing is $ per hour.

Make sure your rate is a reduced fraction or an integer.

19. Determine whether the given points are on the graph of y=−2x+5y=-2x+5.

Select all points that lie on the graph.
• (2,1)
• (6,-14)
• (-1,3)
• (-1,7)

20. The equation of the line with xx-intercept 22 and yy-intercept −2-2 can be written in the form y=mx+by=mx+b where
the number mm is:
the number bb is:

21. Graph the following equation. y=4x+4y=4x+4

22. Graph the following equation. y=4x−7y=4x-7

23. Graph the following equation. y=−3x+1y=-3x+1

24. Graph the following equation. y=2x−4y=2x-4

25. Graph the equation 2x+3y=92x+3y=9 by writing the equation in the form y=mx+by=mx+b.



• 3-13

State the run, rise, and slope of the line above.

run =

rise =

m =



with poor text formatting, useless repetition, and oh yeah

no indication of any work on your part.

I wonder how much time it took him to type this all out.

M9 Exercise A

1. The point plotted below is located at (4, -4).

Coordinates: (4, -4)

2. To graph the equation x=1, simply draw a vertical line passing through the x-coordinate 1 on the graph.

Graph:

|
|
|
x
|
|
|

3. Fill out the chart and plot the points on the grid for the equation y=x-3:
x | y
---------------
0 | -3
1 | -2
2 | -1
3 | 0

Graph:

(3, 0) (2, -1) (1, -2) (0, -3)
----------------------------------
| | | |
| | | |
| | | |
x x x x

4. To graph the equation y=-1, simply draw a horizontal line passing through the y-coordinate -1 on the graph.

Graph:

---------------
| |
| |
| |
x x

5. Fill in the t-table and plot the points on the grid for the equation -3x+4y=-8:
x | y
--------------
-4 | 4
0 | -2
4 | -8

Graph:

(-4, 4) (0, -2) (4, -8)
--------------------------------------------------
| | |
| | |
| | |
x x x

6. The point (2, 2) lies in quadrant I.

7. Sketch a graph of x+2y=-4:

Graph:

|
| /
| /
|/
x

8. Plot the point (2, 2) on the grid:

Graph:

|
|
|
x
|
|
|

M9 Practice B

1. The correct slope of the line passing through (-5, 4) and (-7, 12) is:
m = (12 - 4) / (-7 - (-5)) = 8 / -2 = -4

2. The run of the line is 14 and the rise is -10. Therefore, the slope is:
m = (-10) / 14 = -5/7

3. The slope of the line that goes through the points (14, 6) and (15, 2) is:
m = (2 - 6) / (15 - 14) = -4 / 1 = -4

4. The slope of the line passing through (9, 2) and (-3, -4) is:
m = (-4 - 2) / (-3 - 9) = -6 / -12 = 1/2

5. The slope of the line is:
m = (-8 - 20) / (-4 - 12) = -28 / -16 = 7/4

6. Match each slope with the type of line it will produce:
-1: Downhill
0: Horizontal
DNE: Vertical

7. The slope of the line shown below is:
m = (-3 - 2) / (-3 - 1) = -5 / -4 = 5/4

8. The slope between the points (-4, 4) and (-2, 4) is 0 since the y-coordinates are the same.

9. The slope of the population growth between the years 1970 and 1988 is:
m = (913600 - 911800) / (1988 - 1970) = 1800 / 18 = 100

10. A line with positive slope and positive y-intercept can be represented by the equation y = mx + b, where m > 0 and b > 0.

For Exercise A:

1. The coordinates of the point plotted below cannot be determined as the question is incomplete. The point is missing the x and y values.

2. To graph the equation x=1, simply draw a vertical line passing through x=1 on the graph.

3. To fill out the chart for the equation y=x-3, substitute the values of x into the equation and solve for y. Then plot each point on the grid.

x | y
----|---
0 | -3
1 | -2
2 | -1
3 | 0

4. To graph the equation y=-1, simply draw a horizontal line passing through y=-1 on the graph.

5. To fill in the table for the equation -3x+4y=-8, substitute the values of x into the equation and solve for y. Then plot each point on the grid.

x | y
-----|---
-4 | 2
0 | -2
4 | -6

6. The point (2,2) lies in quadrant I.

7. To sketch the graph of x+2y=-4, rearrange the equation into slope-intercept form:
2y = -x - 4
y = -1/2x - 2
Sketch a line with a slope of -1/2 passing through the y-intercept of -2.

8. To plot the point (2,2), locate the intersection of the x-axis and y-axis at (0,0) and count 2 units to the right along the x-axis and 2 units up along the y-axis.

For Practice B:

1. The correct slope of the line passing through (-5,4) and (-7,12) is given by the formula:
m = (y2 - y1) / (x2 - x1)
m = (12 - 4) / (-7 - -5)
Simplify the equation to find the slope.

2. The run, rise, and slope of the line 14-10 can be determined by comparing the change in x and y values:
Run = difference in x values = 14 - 10
Rise = difference in y values = -10 - 14
Slope = rise / run

3. The slope of the line passing through the points (14,6) and (15,2) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Substitute the given values and simplify the equation to find the slope.

4. The slope of the line passing through the points (9,2) and (-3,-4) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Substitute the given values and simplify the equation to find the slope.

5. The slope of the line can be found by observing the values given in the graph. Count the rise and run between two points on the graph and use the formula:
Slope = rise / run

6. Match each slope with the corresponding type of line:
-1 -> downhill
0 -> horizontal
DNE -> vertical

7. To find the slope of the line shown in the graph, calculate the rise and run between two points on the line and use the formula:
Slope = rise / run

8. To find the slope between the points (-4,4) and (-2,4), calculate the difference in y values and the difference in x values, then use the formula:
Slope = (y2 - y1) / (x2 - x1)

9. To compute the slope of the population growth (or decline) between the years 1970 and 1988, calculate the difference in population and the difference in years, then use the formula:
Slope = (y2 - y1) / (x2 - x1)

10. To sketch a line with a positive slope and positive y-intercept, draw a line that rises as it moves to the right and intersects the y-axis above the origin.

For Practice Exercise C:

1. The equation of the line with slope 2 and y-intercept 3 can be written in the form y = mx + b, where m represents the slope and b represents the y-intercept.

2. Graph the equation y = -3x + 1 by plotting points on the coordinate plane.

3. Graph the equation y = -x + 4 by plotting points on the coordinate plane.

4. To determine if the given points are on the graph of y = -2x + 5, substitute the x and y coordinates of each point into the equation and check if the equation is true for each point.

5. The slope of the line y = x - 3 can be determined by comparing the coefficient of x in the equation, which represents the slope, and the constant term, which represents the y-intercept.

6. Graph the equation y = 2x - 1 by plotting points on the coordinate plane.

7. Graph the equation -2x + 4y = -20 by rearranging the equation in slope-intercept form y = mx + b.

8. Graph the equation 4x - 5y = 15 by rearranging the equation in slope-intercept form y = mx + b.

9. Graph the equation y = x - 8 by plotting points on the coordinate plane.

10. The slope-intercept form of a linear equation is in the form y = mx + b, where m represents the slope and b represents the y-intercept.