Exercise 4 Page 201

Consider the given equation of a line. y= -4x+1 To find the slope of a line perpendicular to the given one, we need to find the negative reciprocal of -4.

m_1 * m_2 = -1

Substitute

m_1= -4

-4 * m_2 = -1

DivEqn

.LHS /(-4).=.RHS /(-4).

m_2 = -1/-4

DivNegNeg

- a/- b=a/b

m=1/4

We found that 14 is the negative reciprocal of -4. Now we can write a general equation in point-slope form for the lines perpendicular to the given line. y-y_1 = 1/4(x-x_1) Since we know that point (2,-3) should be contained in the our line, we can substitute it for (x_1, y_1). By doing so, we will be able to write the equation of the line perpendicular to the given one, and containing the given point.

y-y_1 = 1/4(x-x_1)

SubstituteII

x_1= 2, y_1= -3

y-( -3) = 1/4(x- 2)

SubNeg

a-(- b)=a+b

y+3=1/4(x-2)

Notice that this is only an example solution, as we could rewrite the equation into other form.