Exercise 30 Page 312

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

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

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Simplify right-hand side

SubNeg

a-(- b)=a+b

m=2-3/1+3

AddSubTerms

Add and subtract terms

m=- 1/4

MoveNegNumToFrac

Put minus sign in front of fraction

m=-1/4

We have found that m = - 14. Now that we know the slope, we can write a partial equation of the line. y= -1/4 x +b To complete the equation, we also 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 ( 1, 2).

y=-1/4x+b

SubstituteII

x= 1, y= 2

2=-1/4( 1)+b

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Solve for b

MultByOne

a * 1=a

2=-1/4+b

AddEqn

LHS+1/4=RHS+1/4

2+1/4=b

NumberToFrac

a = 4* a/4

8/4+1/4=b

AddFrac

Add fractions

9/4=b

RearrangeEqn

Rearrange equation

b=9/4

We have found that b = 94. We can now complete the equation. y=-1/4x+9/4