Warm up:

1 2 3 4

Positive Slope Negative Slope Slope of 0 No Slope

Section 2.1 – Linear Equations in Two Variables

Based upon each graph below, identify the slope as positive,negative, zero, or no slope/undefined.

y = mx + bm is positive

y = -mx + bm is negative

y = km is zero

x = km is undefined

Section 2.1 – Linear Equations in Two Variables

After this section you should be able to:

• Calculate the slope of a line given two points.

• Write the equation of a line (in Point – Slope Form).

• Write the equation of a line (in Standard Form). Ax+By = C

1 1y y m x x

• Solve real-world problems using linear equations.

• Use slope to identify parallel and perpendicular lines

1 2

1 2

y ym

x x

a) Find the slope of the line given the two pointsb) Comment briefly on the graph of the line connecting the two points. (up to the right, down to the right, vertical, or horizontal)

3, 6 , 2, 7

7 6 1

m2 3 5

graph is up to right

(2, 0), (8, 12)

12 0m 2

8 2

graph is up to right

5, 9 , 5,12

12 9m und.

5 5

Vertical; x = 5

• Calculate the slope of a line given two points.

1 2

1 2

y ym

x x

a) Find the slope of the line given the two pointsb) Comment briefly on the graph of the line connecting the two points. (up to the right, down to the right, vertical, or horizontal)

2, 3 , 4, 3

3 3m 0

4 2

Horizontaly = -3

(-1, 5), (2, 4)

4 5 1

m2 1 3

graph is downto right

5, 9 , 5,12

12 9u d.

5m

5n

Verticalx = 5

• Calculate the slope of a line given two points.

ALL Equations – Point Slope Form 1 1y y m x x

Find the equation of the line which passes through (2, 3) and (3, 5)

5 3m 2

3 2

y 3 2 x 2

or

y 5 2 x 3

Find the equation of the line which passes through (3, 0) and (3, 3)3 0

m und3 3

x 3

Find the equation of the line which passes through (6, 7) and (2, 7)

7 7m 0

2 6

y 3

• Write the equation of a line (in Point – Slope Form)

Find the equation of the line with slope 5 passing through (3, -1)

y 1 5 x 3

Find the equation of the line passing through (2, 3) and (7, 5)

5 3 2m

7 2 5

2y 3 x 2

5or

2y 5 x 7

5

Find the equation of the line passing through (4, 6) and (4, -1)

6 1m und

4 4

x 4

Parallel Lines – Same Slope 1 2m m

Normal Lines – Negative/Reciprocal Slopes 12

1m

m

Determine if the lines connecting the two points below are parallel,perpendicular, or neither.

2, 3 , 2, 4 1, 5 , 7, 3

4 3 1m

2 2 4

5 3 2 1

m1 7 6 3

neither

Determine if the lines connecting the two points below are parallel,perpendicular, or neither.

6, 2 , 9, 3 1,11 , 3, 53 2 1

m9 6 3

5 11 6

m 33 1 2

perpendicular

Find the equation of the line parallel to 2x – 5y = -3 whichpasses through (3, 1).

2x 5y 3

5y 2x 3

y x2

5

2y 1 x 3

5

Rewrite your equation in Standard Form (Ax + By = C).

2x1 3y

5

xy 35 1 2

xy 65 5 2 1 2x 5y

2x 5y 1

Find the equation of the line perpendicular to 7x – y = 4 whichpasses through (2, -5).

7x y 4

y 7x 4

y 7x 4

1y 5 x 2

7

Rewrite your equation in Ax + By = C form.

1y 5 x

72

xy 25 17

xy 27 35

x 7y 33

Your salary was $28,500 in 1998 and $32,900 in 2000. If your salary follows a linear growth pattern, what will your salarybe in 2003?

32900 28500m 2200

2000 1998

y 28500 2200 x 1998

y 28500 2200 2003 1998 y $39,500

(1998, 28,500) (2000, 32,900)

1 2

1 2

y ym

x x

(2003, ???)

Use your equation to predict the salary for 2003

1 1y y m x x

x = y =

year salary

Use your equation to predict the salary for 2003

A business purchases a piece of equipment for $875. After 5 years the equipment will be outdated and have no value. Writea linear equation giving the value V of the equipment during the5 years it will be used.

(0, 875) and (5, 0)

875 0m 175

0 5

y 875 175 x 0

1 2

1 2

y ym

x x

1 1y y m x x

x = y =

years since purchasing Value (V)

This equation represents Value (V)

A contractor purchases a piece of equipment for $36,500. Theequipment requires an average expenditure of $5.25 per hourfor fuel and maintenance, and the operator is paid $11.50 per hour.

a) Write a linear equation giving the total cost C of operating this equipment for t hours.

C 36,500 5.25t 11.50t

C 16.75t 36500

b) Assuming that customers are charged $27 per hour of machine use, an equation which represents the profit.

P R C P 27t 16.75t 36500

c) Find the ‘break-even’ point.

0 27t 16.75t 36500

t 3,561 hours

Section 2.1 – Linear Equations in Two Variables

After this section you should be able to:

• Calculate the slope of a line given two points.

• Write the equation of a line (in Point – Slope Form).

• Write the equation of a line (in Standard Form). Ax+By = C

1 1y y m x x

• Solve real-world problems using linear equations.

Homework: Pg. 181 #29, 30, 33, (74-75 standard form), 78, 79

• Use slope to identify parallel and perpendicular lines

Quiz 2.1 FRIDAY