Exercise 20 Page 532

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, y=- 2/3x, will have a slope of 32. With this information, we can write a general equation for all lines with a slope perpendicular to that of the given equation: y=3/2x+b. We are asked to write the equation of a line perpendicular to the given equation that passes through the given point. If we substitute (2,2) into the general equation, we can solve for the y-intercept of the perpendicular line.

y=3/2x+b

SubstituteII

x= 2, y= 2

2=3/2* 2+b

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Solve for b

FracMultDenomToNumber

a/2* 2 = a

2=3+b

SubEqn

LHS-3=RHS-3

- 1=b

RearrangeEqn

Rearrange equation

b=- 1

Now that we have the y-intercept, we can write the equation for the perpendicular line representing the bike path: y=3/2x-1