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Warm-up 8/13/12. A cell phone company charges a $20 flat fee plus $0.05 for every minute used for calls. Make a table of values from 0 to 60 minutes in 10 -minute intervals that represent the total amount charged. Write an algebraic equation that could be used to represent the situation.
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Warm-up 8/13/12 A cell phone company charges a $20 flat fee plus $0.05 for every minute used for calls. Make a table of values from 0 to 60 minutes in 10-minute intervals that represent the total amount charged. Write an algebraic equation that could be used to represent the situation. What do the unknown values in your equation represent?
Make a table of values from 0 to 60 minutes in 10-minute intervals that represent the total amount charged.
Write an algebraic equation that could be used to represent the situation. • y = 0.05x + 20 • What do the unknown values in your equation represent? • x represents the number of minutes used, and y represents the total amount charged.
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 • (5, 0) • (0, -5) | | | | | 1 2 3 4 5 | | | | | a
(12, 0) (0, -6) 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 = 12 x-intercept: x – 2(0) = 12 x = 12 y-intercept: 0 – 2y = 12 -2y = 12 y = -6
(3, 0) (0, ) y = Find the x- and y-intercepts. 3) 3x – 5y = 9 x-intercept: 3x – 5(0) = 9 3x = 9 x = 3 y-intercept: 3(0) – 5y = 9 -5y = 9
(0, 7) Find the x- and y-intercepts. 4) y = 7 x-intercept: 0 = 7 Does Not Exist (DNE) y-intercept: y = 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.
Slope Formula: given two points (x1, y1) and (x2, y2) on a line, the slope m can be found as follows: where, x1≠ x2.
Slope: Negative Slope: Positive Slope: Zero Slope: Undefined
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
y = 3x + 1 Write in slope-intercept form. 5) m = 3, y-intercept = 1
6) 7) m = , y-intercept: (0, 0) Find the slope and y-intercept of the following equation. m = 3, y-intercept: (0, -7)
Example (8) 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) cont. 2. Identify the slope and y-intercept: The slope is the rate or charge for “each” pencil Slope (m) = 0.50 The y-intercept is a starting value. The store paid $10. So the starting revenue then is -$10 y-intercept (b) = -10
Example (8) cont. 3. Substitute the slope and y-intercept into the equation y = mx + b. m = 0.50 b = -10 y = 0.50x - 10 4. Change the slope into a fraction for graphing and rewrite the equation using the fraction.
5. Set up the coordinate plane and identify the independent and dependent variables. x represents the number of pencils sold and is the independent variable. The x-axis label is “Number of pencils sold”. y represents the revenue in dollars and is the dependent variable. The y-axis label is “Revenue in dollars ($)”.
6. Plot points using a table of values. -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.