Exercise 23 Page 166

When lines are perpendicular, their slopes will be opposite reciprocals of one another. With this, we know that all lines that are perpendicular to our given line will have a slope of - 14. Given Slope:& m_1=4 Opposite Reciprocal:& m_2=- 14 With this information, we can write a general equation for all lines with a slope perpendicular to that of the given equation. y= -1/4x+ b To determine the value of b, we can use the fact that our line must pass through point (8,2). Let's substitute x= 8 and y= 2 into the equation and solve for b.

y=-1/4x+b

SubstituteII

x= 8, y= 2

2=-1/4( 8)+b

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Solve for b

MoveRightFacToNumOne

1/b* a = a/b

2 = -8/4+b

CalcQuot

Calculate quotient

2 = -2 +b

AddEqn

LHS+2=RHS+2

4 = b

RearrangeEqn

Rearrange equation

b= 4

Now that we have the y-intercept, we can write the equation for the perpendicular line. y= -1/4x+ 4