Exercise 48 Page 191

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. (- 4,2) and (6, - 3) To determine the slope of the line, we use the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( - 4, 2) & ( 6, - 3)

m=- 3-( 2)/6-( - 4)

▼

Simplify right-hand side

SubNeg

a-(- b)=a+b

m=- 3-2/6+4

AddSubTerms

Add and subtract terms

m=- 5/10

ReduceFrac

a/b=.a /5./.b /5.

m=- 1/2

MoveNegDenomToFrac

Put minus sign in front of fraction

m=- 1/2

Now that we know the slope of the line is - 12, 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 ( - 4, 2).

y-y_1=m(x-x_1)

SubstituteValues

Substitute values

y- 2= -1/2(x-( - 4))

SubNeg

a-(- b)=a+b

y-2=- 1/2(x+4)

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

y-2=- 1/2(x+4)

AddEqn

LHS+2=RHS+2

y-2+2=- 1/2(x+4)+2

▼

Rewrite

AddTerms

Add terms

y=- 1/2(x+4)+2

Distr

Distribute - 1/2

y= - 1/2x +(- 1/2)4 +2

MultNegPos

(- a)b = - ab

y= - 1/2x +(- 1/2* 4) +2

MoveRightFacToNum

a/c* b = a* b/c

y = - 1/2x+(- 4/2) +2

AddNeg

a+(- b)=a-b

y = - 1/2x-4/2+2

CalcQuot

Calculate quotient

y = - 1/2x-2 +2

AddTerms

Add terms

y= - 1/2x

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!