A cell phone company charges a $20 flat fee plus $0.05 for every minute used for calls.

1. Make a table of values from 0 to 60 minutes in 10-minute intervals that represent the total amount charged.

2. Write an algebraic equation that could be used to represent the situation.

3. What do the unknown values in your equation represent?

Warm-up 8/13/12

1. Make a table of values from 0 to 60 minutes in 10-minute intervals that represent the total amount charged.

Minutes used Total amount charged ($)

0 20 + 0(0.05) = 20.00

10 20 + 10(0.05) = 20.50

20 20 + 20(0.05) = 21.00

30 20 + 30(0.05) = 21.50

40 20 + 40(0.05) = 22.00

50 20 + 50(0.05) = 22.50

60 20 + 60(0.05) = 23.00

2. Write an algebraic equation that could be used to represent the situation.• y = 0.05x + 20

3. What do the unknown values in your equation represent?• x represents the number of minutes used, and y

represents the total amount charged.

Creating and Graphing Equations in Two Variables

The x-intercept is the coordinate at which a graph intersects the x-axis.

The y-intercept is the coordinate at which a graph intersects the y-axis.

Example 1:

a) State the x-intercept

b) State the y-intercept

1) Line a

a) (5, 0)

b) (0, -5)

a

1 2 3 4 5 | | | | | | | | | |

Let y = 0 to find the x-intercept.

Let x = 0 to find the y-intercept.

Find the x- and y-intercepts.

2) x – 2y = 12x-intercept: x – 2(0) = 12

x = 12

y-intercept: 0 – 2y = 12

y = -6 -2y = 12

(12, 0)

(0, -6)

Find the x- and y-intercepts.

3) 3x – 5y = 9

x-intercept: 3x – 5(0) = 9 3x = 9

y-intercept: 3(0) – 5y = 9

-5y = 9

x = 3

y = 5

9

(3, 0)

(0, )5

9

Find the x- and y-intercepts.

4) y = 7

x-intercept: 0 = 7Does Not Exist (DNE)

y-intercept: y = 7 (0, 7)

Slope: is the ratio of the rise to the run as you move from one point to another along a line.

• Rise: the difference between the y-coordinates of two points

• Run: the difference between the x-coordinates of two points

The slope, m, of a line is the ratio of the change in the y-coordinate to the corresponding change in the x-coordinates.

x

y

run

riseslope(m)

Slope Formula: given two points (x1, y1) and (x2, y2) on a line, the slope m can be found as follows:

12

12slope(m)xx

yy

where, x1 ≠ x2.

Slope:

Positive

Slope:

Undefined

Slope:

Zero

Slope:

Negative

Slope-Intercept Form

Given the slope m and the y-intercept b of a a line, the slope-intercept form of an equation of a line is:

y = mx + b

Write in slope-intercept form.

5) m = 3, y-intercept = 1

y = 3x + 1

Find the slope and y-intercept of the following equation.

6) 73 xy

m = 3, y-intercept: (0, -7)

7) xy3

2

m = , y-intercept: (0, 0) 3

2

A local convenience store owner spent $10 on pencils to resell at the store. What is the equation of the stores revenue if each pencil sells for $0.50? Graph the equation.

1. Identify the known quantities:Initial cost of pencils: $10

Charge per pencil: $0.50

Example (8)

2. Identify the slope and y-intercept:

The slope is the rate or charge for “each” pencilSlope (m) = 0.50

The y-intercept is a starting value. The store paid $10. So the starting revenue then is -$10

y-intercept (b) = -10

Example (8) cont.

3. Substitute the slope and y-intercept into the equation y = mx + b.

4. Change the slope into a fraction for graphing and rewrite the equation using the fraction.

2

1

100

5050.0 m

102

1 xy

Example (8) cont.

m = 0.50 b = -10

y = 0.50x - 10

5. Set up the coordinate plane and identify the independent and dependent variables.

x represents the number of pencils sold and is the independent variable. The x-axis label is “Number of pencils sold”.

y represents the revenue in dollars and is the dependent variable. The y-axis label is “Revenue in dollars ($)”.

6. Plot points using a table of values.

x y

0

2

4

6

-10-9-8

-7

Example 9: A taxi company in Atlanta charges $2.50 per ride plus $2 for every mile driven.Write and graph an equation that models this scenario.1. Determine the known quantities.

2. Identify the slope and y-intercept.

3. Substitute the slope and y-intercept into the equation y = mx + b.

4. Set up the coordinate plane and identify the independent and dependent variables.

5. Graph the equation for the line using the slope and y-intercept.