Exercise 15 Page 243

When lines are parallel, they have the same slope. Let's consider the given equation. y=-3/4x+4 The slope of the line represented by the above equation is - 34. Therefore, the slope of any parallel line will also be - 34. y=-3/4x+b To find the equation of a parallel line through the point ( - 2, 3), we will substitute ( - 2, 3) for x and y respectively, in the above formula.

y=-3/4x+b

SubstituteII

x= - 2, y= 3

3=-3/4( - 2)+b

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Solve for b

MultNegNegOnePar

- a(- b)=a* b

3=3/4*2 +b

MoveRightFacToNum

a/c* b = a* b/c

3=6/4+b

ReduceFrac

a/b=.a /2./.b /2.

3=3/2+b

SubEqn

LHS-3/2=RHS-3/2

3-3/2=b

WriteAsFrac

Write as a fraction

6/2-3/2=b

SubFrac

Subtract fractions

3/2=b

RearrangeEqn

Rearrange equation

b=3/2

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Write fraction as a mixed number

WriteSum

Write as a sum

b=2+1/2

WriteSumFrac

Write as a sum of fractions

b=2/2+1/2

QuotOne

a/a=1

b=1+1/2

AddTerms

Add terms

b=1 12

Now that we know the y-intercept is 1 12, we can write the equation of the parallel line through the given point. y=-3/4x+ 1 12