Exercise 9 Page 181

Equations in point-slope form follow a specific format. y- y_1= m(x- x_1) In this form, m is the slope of the line and ( x_1, y_1) is a point on the line. Let's choose two points from the given table. (3,1) and (7,-5) To determine the slope of the line, we use the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 3,1) & ( 7,-5)

m=-5- 1/7- 3

▼

Simplify right-hand side

SubTerms

Subtract terms

m=-6/4

MoveNegNumToFrac

Put minus sign in front of fraction

m=-6/4

ReduceFrac

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

m=-6/2/4/2

CalcQuot

Calculate quotient

m=-3/2

Now that we know the slope of the line is - 32, we can write the equation of the line in point-slope form. We can use either of the given points as (x_1,y_1) in our equation. Let's use ( 3, 1).

y-y_1=m(x-x_1)

SubstituteValues

Substitute values

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

Please note that any point on the line can be used to form a point-slope equation. Therefore, our equation is only one of infinitely many possible equations!