Exercise 14 Page 243

When lines are parallel, they have the same slope. Let's consider the given equation. y=-1/2x+6 The slope of the line represented by the above equation is - 12. Therefore, the slope of any parallel line will also be - 12. y=-1/2x+b To find the equation of a parallel line through the point ( - 4, 2) we will substitute ( - 4, 2) for x and y, respectively, in the above formula.

y=-1/2x+b

SubstituteII

x= - 4, y= 2

2=-1/2( - 4)+b

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Solve for b

MultNegNegOnePar

- a(- b)=a* b

2=1/2*4+b

MoveRightFacToNumOne

1/b* a = a/b

2=4/2+b

CalcQuot

Calculate quotient

2=2+b

SubEqn

LHS-2=RHS-2

0=b

RearrangeEqn

Rearrange equation

b=0

Now that we know the y-intercept, we can write the equation of the parallel line through the given point. y=-1/2x