Exercise 54 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, C(-4,2) and D(-1,7), using the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( -4,2) & ( -1,7)

m=7 - 2/-1-( -4)

SubNeg

a-(- b)=a+b

m=7-2/-1+4

AddSubTerms

Add and subtract terms

m=5/3

The slope of the line is 53. This means, for every three units to the right we move on a coordinate plane, we move five units up. At this point, we have the following equation. y-y_1 = 5/3(x-x_1) Next, we can substitute either of the points C(-4,2) and D(-1,7) for (x_1, y_1) in the formula above. Let's choose point C.

y-y_1 =5/3(x-x_1)

SubstituteII

x_1= -4, y_1= 2

y- 2 = 5/3(x-( -4))

SubNeg

a-(- b)=a+b

y-2=5/3(x+4)

If, on the other hand, we would choose point D, we would get the following equation of the line. y-7=5/3(x+1)