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Name:__________________________
Algebra 2 PAP Linear Parent Function
Average Rate of Change (Slope)
Graphically:
Rise
Run
m=
Numerically:
y f ( x2 )  f ( x1 )

x
x2  x1
Analytically:
f ( x)  mx  b, m is slope
Parallel lines have the same slope.
Perpendicular lines have opposite reciprocal slopes.
Horizontal lines have a slope of zero.
Vertical lines have an undefined slope.
Practice:
1. Determine the average rate of change between the two linear points (-1, 6) and (-4, 7).
2. Determine the average rate of change for f(3) = 7 and f(5) = 11.
3. Find the average velocity for
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f ( x)  x 2  2 x over the interval [-3, -1].
4. What is the slope of the line perpendicular to the line x = 2?
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5. Determine the average rate of change for 2 x  3 y  17  0 .
1. On the same coordinate grid, graph the following equations: y  2 x and y  2 .
Graphing Linear Equations
Slope-Intercept Form
y = mx + b
1) Make sure the equation is solved for y.
2) m is slope and b is y-intercept (where the point crosses the y-axis)
3) To graph, plot the y-intercept first. At the y-intercept, use the slope to count rise
over run.
Standard Form
Ax + By = C
1) A cannot be a negative number or a fraction.
2) B cannot be a fraction.
3) To graph, use the x-intercept and y-intercept.
4) Identify the x-intercept by letting y = 0 and solving for x.
5) Identify the y-intercept by letting x = 0 and solving for y.
Point-Slope Form
y – y1 = m(x – x1)
1) m is slope and ( x1 , y1 ) is a given coordinate
2) To graph, plot the given point. At the point, use the slope to count rise over run.
Practice:
1. Graph the equation y  
2
x 1
3
2. Graph the equation 5 x  2 y  10
1
3
3. Graph the equation ( y  5)   ( x  2)
Additional Practice: Graph each linear equation below on your own graph paper.
1
1. y   x  3
3
2. y  4 x  2
3.  6 x  3 y  18  0
4. 2 x  3 y  6
(what are the x and y intercepts?)
(what are the x and y intercepts?)
5. y  5 
1
( x  3)
2
6. y  2  2( x  4)
Writing the Equation of a Line
Write the equation of a line when given…
1. Slope and y-intercept
a. Substitute m and b into y = mx + b
1. m = 4 and b = -10
2. Perpendicular to y – 1 = -3/4 (x + 2)
2. A Graph
a. Find the y intercept from the graph
b. Count the slope from the graph
c. Substitute the slope and y intercept in the slope intercept form of the equation.
3. Slope and one point
a. Use the point slope formula
b. Substitute m and the given point into the formula
1. m = -2 and (-1/2,5)
2. || to 3x – 5y = 4 through (-2,10)
4. Two points
a. Calculate the slope of the two points
b. Use one of the points and the slope to substitute into the point slope formula.
1. (-2,5) and (3,-1)
2. (1/2,3/4) and (6,-2/7)
5. x and y intercepts
a. Write the intercepts as ordered pairs
b. Calculate the slope
c. Substitute the slope and the y intercept into the slope intercept formula.
1. x-int (-2,0)
y-int (0,1/2)
Solve Systems of Equations by Graphing
Possibilities for graphs of systems of linear equations:
Case 1: one solution
Case 2: infinite solutions
Case 3: no solution
When solving by graphing, convert both equations to slope-intercept form OR use standard
form graphing with x and y intercepts then graph to find solution.
Example 1 : Solve by graphing
4x  y  8
2 x  3 y  18
Solution __________________
Example 2 : Solve by graphing
Example 3:
2x  y  4
2x  y  1
y = x -2
y = x+2
y=2
y=x
Identify the domain and range of each relation in interval notation. State whether or not each relation
is a function.
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Solving Systems of Equations
by Graphing
Solve the linear systems by graphing. Write your answer as an ordered pair (x, y).
1.
x + 2y = 2
x – 4y = 14
2.
y = 3x + 2
y = 3x - 2
5.
y = -3x - 13
-x – 2y = -4
3.
x – 7y = 6
-3x + 21y
= -18
4.
y = x -1
y = -x + 4
6.
y = x +5
y = -5
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