Exercise 29 Page 312

Start by using the Slope Formula to find the slope.

y=- x+2

Practice makes perfect

Let's start by recalling the slope-intercept form of a line. y= mx+b Here, m is the slope and b is the y-intercept. We will use the two given points to calculate these values. Let's find the slope m by substituting the points into the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( - 2,4) & ( 3,- 1)

m=- 1- 4/3-( - 2)

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Simplify right-hand side

SubNeg

a-(- b)=a+b

m=- 1-4/3+2

AddSubTerms

Add and subtract terms

m=- 5/5

MoveNegNumToFrac

Put minus sign in front of fraction

m=-5/5

QuotOne

a/a=1

m=- 1

Now that we know that the slope is - 1, we can write a partial equation of the line. y= - 1 x +b ⇔ y=- x+b To complete the equation, we need to determine the y-intercept b. Since we know that the given points satisfy the equation, we can substitute one of them and solve for b. Let's use ( - 2, 4).

y=- x+b

SubstituteII

x= - 2, y= 4

4=-( - 2)+b

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Solve for b

NegNeg

- (- a)=a

4=2+b

SubEqn

LHS-2=RHS-2

2=b