Exercise 32 Page 194

Equations in point-slope form all follow the same general format. y-y_1=m(x-x_1) Here m represents the slope of the line and (x_1,y_1) represents any point lying on the line. To write an equation for a line in this form, we must find the slope and substitute either of the given points into the formula. We will begin by finding the slope of the line that connects the given points, (-4,4) and (2,10), using the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( -4,4) & ( 2,10)

m=10 - 4/2-( -4)

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Simplify right-hand side

SubNeg

a-(- b)=a+b

m=10-4/2+4

AddSubTerms

Add and subtract terms

m=6/6

CalcQuot

Calculate quotient

m=1

The slope of the line is 1. This means, for every one unit to the right we move on a coordinate plane, we move one unit up. At this point, we have the following equation. y-y_1=1(x-x_1) ⇔ y-y_1 = x-x_1 We can substitute either of the given points for (x_1,y_1). Therefore, we can give two equally valid answers. y-4=x-(-4) ⇔ y - 4 = x+4 or y-10=x-2