Exercise 55 Page 204

An equation in point-slope form follows a specific format. y-y_1=m(x-x_1) In this form m represents the slope of the line and (x_1,y_1) represents any point lying on the line. We will begin by finding the slope of the line that connects the given points, E(3,-2) and F(-5,-8), using the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 3,-2) & ( -5,-8)

m=-8 - ( -2)/-5- 3

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Simplify right-hand side

SubNeg

a-(- b)=a+b

m=-8+2/-5-3

AddSubTerms

Add and subtract terms

m=-6/-8

DivNegNeg

- a/- b=a/b

m=6/8

ReduceFrac

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

m=3/4

The slope of the line is 34. This means, for every four units to the right we move on a coordinate plane, we move three units up. At this point, we have the following equation. y-y_1 = 3/4(x-x_1) We can substitute either of the points E(3,-2) and F(-5,-8) for (x_1, y_1) in the formula above. Let's choose point E.

y-y_1 =3/4(x-x_1)

SubstituteII

x_1= 3, y_1= -2

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

SubNeg

a-(- b)=a+b

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

If, on the other hand, we would choose point F, we would get the following equation of the line. y+8=3/4(x+5)