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Pearson Algebra 2 Common Core, 2011
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Pearson Algebra 2 Common Core, 2011 View details
3. Linear Functions and Slope-Intercept Form
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Exercise 57 Page 79

Practice makes perfect
a Let's start by reviewing how to find the slope of a line. The slope is the ratio of the vertical change to the horizontal change between the points ( x_1, y_1) and ( x_2, y_2).
Slope &=& &Vertical change (rise)/Horizontal change (run) &=& &y_2-y_1/x_2-x_1

We can use the graph to find the coordinates of the points P and Q.

We can now find the slope using these points and the Slope Formula.
m = y_2-y_1/x_2-x_1
SubstitutePoints

Substitute ( -3,-5) & ( 0,-2)

m = -2-( -5)/0-( -3)
SubNeg

a-(- b)=a+b

m = -2+5/0+3
AddSubTerms

Add and subtract terms

m = 3/3
CalcQuot

Calculate quotient

m = 1
We found that the slope between P and Q is m=1.
b We will proceed just as we did in Part A.
We will use the given graph to find the coordinates of the points Q and S.
Now, we can find the slope by using the Slope Formula.
m = y_2-y_1/x_2-x_1
SubstitutePoints

Substitute ( 0,-2) & ( 4,2)

m = 2-( -2)/4- 0
SubNeg

a-(- b)=a+b

m = 2+2/4 -0
AddSubTerms

Add and subtract terms

m = 4/4
CalcQuot

Calculate quotient

m = 1
We found that the slope between Q and S is m=1.
c Once more, we will use the given graph to find the coordinates of the points S and P.
Now, we can find the slope by using the Slope Formula.
m = y_2-y_1/x_2-x_1
SubstitutePoints

Substitute ( 4,2) & ( -3,-5)

m = -5- 2/-3- 4
SubTerms

Subtract terms

m = -7/-7
CalcQuot

Calculate quotient

m = 1
The slope between P and S is m=1.
d Finally, we will use the given graph to find the coordinates of the points R and Q.
Now, we can find the slope by using the Slope Formula.
m = y_2-y_1/x_2-x_1
SubstitutePoints

Substitute ( 1,-1) & ( 0,-2)

m = -2-( -1)/0-( 1)
SubNeg

a-(- b)=a+b

m = -2+1/0-1
AddSubTerms

Add and subtract terms

m = -1/-1
CalcQuot

Calculate quotient

m = 1
The slope between R and Q is m=1.
e As we can see from the previous parts of this exercise, the slope between all the pair of points given was the same, m=1. Notice that all these points lie on the same line. We can conclude that the slope between any pair of collinear points is the same.
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arrow_right Lesson Check p.78
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Lesson Check 2 (Page 78)
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arrow_right Practice and Problem-Solving Exercises p.78-80
Practice and Problem-Solving Exercises 8 (Page 78)
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Standardized Test Prep 66 (Page 80)
arrow_right Mixed Review p.80
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