Integrated Math 2 Unit 1 - Quiz

Integrated Math 2 – Unit 1 – Prep for Quiz Fall 2011

Name ______ Itg2 U1 PQz1

Answer the following questions using complete sentences

1. Name the three equations used for a line and write the equations in the correct format.

Modified Point-Slope: y = m(x – x1) + y1

Slope-Intercept: y = mx + b

Standard Form: Ax + By = C

For each pair of points below, find the slope.

2. (4, 2) and (7, 3)

Slope (m) = D y Change in y’s

D x Change in x’s

m = (y2) – (y1)

(x2) – (x1)

m = (3) – (2)

(7) – (4)

m = 1/3

3. (- 1, 5) and (6, - 4)

Slope (m) = D y Change in y’s

D x Change in x’s

m = (y2) – (y1)

(x2) – (x1)

m = (5) – (- 4)

(-1) – (6)

m = 9/- 7

4. (- 5, 3) and (2, - 11)

Slope (m) = D y Change in y’s

D x Change in x’s

m = (y2) – (y1)

(x2) – (x1)

m = (3) – (- 11)

(- 5) – (2)

m = 14/- 7

m = - 2

Write the equation of the line for each problem below (5 – 11) in ALL three forms.

5. Find the equation of the line with a slope of 3 and passes through (-2, 4)

Modified point slope: y = m (x – x1) + y1

y = 3(x – - 2) + 4

y = 3(x + 2) + 4

Slope – Intercept: y = mx + b

y = 3x + 6 + 4 (Use Mod. Pt slope)

y = 3x + 10

Standard Form: Ax + By = C

3x – y = - 10

6. Find the equation of the line with a slope of 2/3 and passes through (-9, -2)

Modified point slope: y = m (x – x1) + y1

y = 2/3 (x – - 9) – 2

y = 2/3 (x + 9) – 2

Slope – Intercept: y = mx + b

y = 2/3 x + 6 – 2 (Use Mod. Pt slope)

y = 2/3 x + 4

Standard Form: Ax + By = C

2/3 x – y = - 4

2x – 3y = -12

7. Find the equation of the line that has a slope of 3/5 and passes through the point (15, 7)

Modified point slope: y = m (x – x1) + y1

y = 3/5 (x – 15) + 7

Slope – Intercept: y = mx + b

y = 3/5 x – 9 + 7 (Use Mod. Pt slope)

y = 3/5 x – 2

Standard Form: Ax + By = C

3/5 x – y = 2

3x – 5y = 10

8. Find the equation of the line that passes through the points (2, 1) and (-3, -9)

Slope (m) = D y Change in y’s

D x Change in x’s

m = (y2) – (y1)

(x2) – (x1)

m = (1) – (- 9)

(2) – (- 3)

m = 10/5

m = 2

Modified point slope: y = m (x – x1) + y1

y = 2(x – 2) + 1 Or y = 2(x + 3) – 9

Slope – Intercept: y = mx + b

y = 2x – 4 + 1 Or y = 2x + 6 – 9

y = 2x – 3 = y = 2x – 3

Standard Form: Ax + By = C

2x – y = 3


9. Find the equation of the line that passes through the points (-1, - 3) and (1, - 1)

Slope (m) = D y Change in y’s

D x Change in x’s

m = (y2) – (y1)

(x2) – (x1)

m = (- 1) – (- 3)

(1) – (- 1)

m = 2/2

m = 1

Modified point slope: y = m (x – x1) + y1

y = 1(x + 1) – 3 Or y = 1(x – 1 ) – 1

Slope – Intercept: y = mx + b

y = 1x + 1 – 3 Or y = 1x – 1 – 1

y = x – 2 = y = x – 2

Standard Form: Ax + By = C

2x – y = 2

10. Find the equation of the line that passes through the points (-2, 7) and (2, -1)

Slope (m) = D y Change in y’s

D x Change in x’s

m = (y2) – (y1)

(x2) – (x1)

m = (7) – (- 1)

(- 2) – (2)

m = 8/- 4

m = - 2

Modified point slope: y = m (x – x1) + y1

y = - 2(x + 2) + 7 Or y = - 2(x – 2) – 1

Slope – Intercept: y = mx + b

y = - 2x – 4 + 7 Or y = - 2x + 4 – 1

y = - 2x + 3 = y = - 2x + 3

Standard Form: Ax + By = C

2x + y = 3

11. A city mouse earns five cheese crumbs for every visitor she scares. After she scared 3 people she had 27 crumbs stored.

Slope (m) = 5 Point (3, 27)

Modified point slope: y = m (x – x1) + y1

y = 5(x – 3) + 27

Slope – Intercept: y = mx + b

y = 5x – 15 + 27

y = 5x + 12

Standard Form: Ax + By = C

5x – y = - 12

12. You currently have $300 in your savings account. Each month you deposited $20.

Slope (m) = 20 Point (0, 300)

Modified point slope: y = m (x – x1) + y1

y = 20(x – 0) + 300

Slope – Intercept: y = mx + b

y = 20x + 300

Standard Form: Ax + By = C

20x – y = - 300

13. A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. Do Not Solve, but do write both equations in all three forms.

Modified point slope: y = m (x – x1) + y1

Equation 1 Equation 2

x + y = 20 3x + 11y = 100

Slope – Intercept: y = mx + b

y = - x + 20 11y = - 3x + 100

11y = - 3x + 100

11 11

y = - 3/11 x + 100/11

Standard Form: Ax + By = C

x + y = 20

14. Using the formula for slope, derive the formula for the modified point slope equation.

Slope (m) = D y Change in y’s

D x Change in x’s

m = (y2) – (y1)

(x2) – (x1)

m (x1 – x2) = (y1 – y2)

y1 – y2 = m (x1 – x2)

+ y2 + y2

y1 = m (x1 – x2) + y2

y = m (x – x1) + y1

15. In question 11 explain what the slope and y-intercept signify.

Slope – Intercept: y = mx + b

y = 5x + 12

The slope 5 which means the rate of change.

(The mouse earns five cheese crumbs for every visitor)

The y-intercept of 12 means how much cheese the mouse had before earning more cheese for scaring people.

(The mouse had 12 before scarring anyone)


Integrated Math 2 – WS 1-1 – Slope WS

Name ______ Itg2 U1 WS1.1

1. Slope is a ratio. Using complete thoughts describe what the ratio of slope represents.

The slope means the rate of change. It describes its steepness, incline, or grade. A higher slope value indicates a steeper incline.

The slope is defined as the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line. Given two points (x1,y1) and (x2,y2) on a line.

Slope (m) = D y Change in y’s

D x Change in x’s

For each problem below, use the slope formula to find the slope of the line that goes between the two given points.

2. (3, 2) and (5, 7)

Slope (m) = D y Change in y’s

D x Change in x’s

m = (y2) – (y1)

(x2) – (x1)

m = (7) – (2) 7 is the highest y value

(5) – (3) (My preference)

m = 5/2

3. (2, 3) and (5, 7)

Slope (m) = D y Change in y’s

D x Change in x’s

m = (y2) – (y1)

(x2) – (x1)

m = (7) – (3)

(5) – (2)

m = 4/3

4. (2, 3) and (7, 5)

Slope (m) = D y Change in y’s

D x Change in x’s

m = (y2) – (y1)

(x2) – (x1)

m = (5) – (3)

(7) – (2)

m = 2/5

5. (3, -2) and (-5, 7)

Slope (m) = D y Change in y’s

D x Change in x’s

m = (y2) – (y1)

(x2) – (x1)

m = (7) – (- 2)

(- 5) – (3)

m = 9/- 8 or m = - 9/ 8

6. (-3, 2) and (-5, 7)

Slope (m) = D y Change in y’s

D x Change in x’s

m = (y2) – (y1)

(x2) – (x1)

m = ( 7 ) – ( 2 )

(- 5) – (- 3)

m = 5/- 2 or m = - 5/ 2

7. (3, -2) and (-5, -7)

Slope (m) = D y Change in y’s

D x Change in x’s

m = (y2) – (y1)

(x2) – (x1)

m = (- 2) – (- 7 )

( 3 ) – (- 5)

m = 5/8

8. (-3, -2) and (5, -7)

Slope (m) = D y Change in y’s

D x Change in x’s

m = (y2) – (y1)

(x2) – (x1)

m = (- 2) – (- 7 )

(- 3) – ( 5 )

m = 5/- 8 or m = - 5/ 8

9. (-3, -2) and (-5, -7)

Slope (m) = D y Change in y’s

D x Change in x’s

m = (y2) – (y1)

(x2) – (x1)

m = (- 2) – (- 7 )

(- 3) – (-5)

m = 5/2

10. (-3, 2) and (5, -7)

Slope (m) = D y Change in y’s

D x Change in x’s

m = (y2) – (y1)

(x2) – (x1)

m = ( 2 ) – (- 7)

(- 3) – ( 5 )

m = 9/- 8 or m = - 9/ 8


For each problem below, identify the y-intercept and the slope. Then describe the direction and steepness of the line from left to right.

11. f(x) = 2x – 3

Slope (m) = 2, y-intercept (b) = -3

The direction of the line can be determined by the slope. Since the slope is positive the line goes from lower left to upper right. The steepness of the line is also determined from the slope. A higher slope value indicates a steeper incline. This slope equals 2, meaning the line goes up 2 units for every 1unit it goes to the right (Or down 2 units for every 1 unit the line goes to the left). The y-intercept is where the line crosses the Y axis of a graph (the x-value is 0 at this point).

12. y = 3/8 x + 2

Slope (m) = 3/8, y-intercept (b) = 2

Since the slope is positive the line goes from lower left to upper right. A lower slope value indicates a line that is not very steep. This slope of 3/8, means the slope is not steep and only goes up 3 units for every 8 unit it goes to the right

13. y = - 1/3 x – 7

Slope (m) = - 1/3, y-intercept (b) = - 7

Since the slope is negative the line goes from upper left to lower right. A lower slope value indicates a line that is not very steep. This slope of - 1/3, means the slope is not steep and only goes down 1 unit for every 3 unit it goes to the right

14. f(x) = - x + 2

Slope (m) = - 1, y-intercept (b) = 2

Since the slope is negative the line goes from upper left to lower right. A slope value of 1indicates the line goes down 1 unit for every 1 unit it goes to the right


Integrated Math 2 – WS 1-2 – Three Equations of a Line

Name ______ Itg2 U1 WS1.2

1. We have discussed three different types of linear equations, identify and describe the three types of equations (Or put in equation format).

Modified Point-Slope: y = m(x – x1) + y1

Slope-Intercept: y = mx + b

Standard Form: Ax + By = C

For each situation below, write the equation of the line in all three forms (modified point-slope form, slope intercept form, and standard form).

2. m = 3, (-2, 4)

Modified Point Slope: y = m (x – x1) + y1

y = 3(x – -2) + 4

y = 3(x + 2) + 4

Slope – Intercept: y = mx + b

y = 3(x + 2) + 4 (Simplify MPS)

y = 3x + 6 + 4

y = 3x + 10

Standard Form: Ax + By = C

y = 3x + 10 (X & Y are whole # and X is Positive)

3x – y = - 10

3. m = - 3/5 , (15, 7)

Modified Point Slope: y = m (x – x1) + y1

y = - 3/5 (x – 15) + 7

Slope – Intercept: (Simplify MPS)

y = mx + b

y = - 3/5 x + 9 + 7

y = - 3/5 x + 16

Standard Form: (X & Y are whole # and X is Positive)

Ax + By = C

y = - 3/5 x + 16

3/5 x + y = 16

3x + 5y = 80

4. m = -2, (-1, -3)

Modified Point Slope: y = m (x – x1) + y1

y = -2(x – -1) – 3

y = -2(x + 1) – 3

Slope – Intercept: (Simplify MPS)

y = mx + b

y = -2x – 2 – 3

y = -2x – 5

Standard Form: (X & Y are whole # and X is Positive)

Ax + By = C

y = -2x – 5

2x + y = - 5

5. m = 1, (-4, 7)

Modified Point Slope: y = m (x – x1) + y1

y = 1(x – -4) + 7

y = 1(x + 4) + 7

Slope – Intercept: (Simplify MPS)

y = mx + b

y = x + 4 + 7

y = x + 11

Standard Form: (X & Y are whole # and X is Positive)

Ax + By = C

x – y = - 11

6. m = - 1/3, (6, -2)

Modified point slope: y = m (x – x1) + y1

y = - 1/3 (x – 6) – 2

Slope – Intercept: y = mx + b

y = - 1/3 x + 2 – 2 (Use Mod. Pt slope)

y = - 1/3 x

Standard Form: Ax + By = C

1/3 x + y = 0

x + 3y = 0

7. m = 2/3 , (-9, -2)

Modified point slope: y = m (x – x1) + y1

y = 2/3 (x + 9) – 2 Think: – (-9) = + 9

Slope – Intercept: y = mx + b

y = 2/3 x + 6 – 2

y = 2/3 x + 4

Standard Form: Ax + By = C

2/3 x – y = - 4

2x – 3y = - 12

8. m = 2, (-2, -2)

Modified point slope: y = m (x – x1) + y1

y = 2(x + 2) – 2 Think: – (-2) = + 2

Slope – Intercept: y = mx + b

y = 2x + 4 – 2

y = 2x + 2

Standard Form: Ax + By = C

2x – y = - 2

9. m = -1, (7, -9)

Modified point slope: y = m (x – x1) + y1

y = - 1(x – 7) – 9

Slope – Intercept: y = mx + b

y = - x + 7 – 9

y = - x – 2

Standard Form: Ax + By = C

x + y = - 2

10. After 12 weeks of saving, you have $300 in your savings account. Each month you deposit $20.

Slope (m) = 20 Point (12, 300)

Modified point slope: y = m (x – x1) + y1

y = 20(x – 12) + 300

Slope – Intercept: y = mx + b

y = 20x – 240 + 300

y = 20x + 60

Standard Form: Ax + By = C

20x – y = - 60


Integrated Math 2 – WS 1-3 – Three Equations of a Line

Name ______ Itg2 U1 WS1.3

1. Equivalence means that two quantities are the same. Explain how you know all three forms of the equation represent the same line.

The equation in any of these three forms can be manipulated to equal another of these formulas.

For each set of points below, write the equation of the line in slope-intercept form.

2. (-4, 6) and (8, 12)

There are actually two easy methods to do this but both methods first solve for slope in the same way.

Slope (m) = D y Change in y’s