Exercise 7 Page 211

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. Here we are given that the line passes through two known points. (- 3,2) and (6, - 1) To determine the slope of the line, we use the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 6, - 1) & ( - 3, 2)

m=2-( -1)/-3- 6

▼

Simplify right-hand side

SubNeg

a-(- b)=a+b

m=2+1/-3-6

AddSubTerms

Add and subtract terms

m=3/-9

ReduceFrac

a/b=.a /3./.b /3.

m=1/-3

MoveNegDenomToFrac

Put minus sign in front of fraction

m=- 1/3

Now that we know the slope of the line is - 13, 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, 2).

y-y_1=m(x-x_1)

SubstituteValues

Substitute values

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

SubNeg

a-(- b)=a+b

y-2=- 1/3(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!

Extra

A Unique Equation

Since any point on the line could be used to form a point-slope equation, there are infinitely many possible equations. If we wanted to write a unique equation for this line, we can rewrite it into slope-intercept form.

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

Distr

Distribute - 1/3

y-2=- 1/3x-1/3*3

FracMultDenomToNumber

a/3* 3 = a

y-2=- 1/3x-1

AddEqn

LHS+2=RHS+2

y=- 1/3x+1