Exercise 5 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. (-5,5) and (-1,1) To determine the slope of the line, we use the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

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

m=1- 5/-1-( -5)

▼

Simplify right-hand side

SubNeg

a-(- b)=a+b

m=1-5/-1+5

AddSubTerms

Add and subtract terms

m=-4/4

MoveNegNumToFrac

Put minus sign in front of fraction

m=-4/4

QuotOne

a/a=1

m= -1

Now that we know the slope of the line is -1, 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 ( -5, 5).

y-y_1=m(x-x_1)

SubstituteValues

Substitute values

y- 5= -1(x-( -5))

SubNeg

a-(- b)=a+b

y-5=-1(x+5)

Since any point on the line could be used to form a point-slope equation, there are infinitely many possible equations. However, we are asked to write the equation in slope-intercept form, so this will give us a unique equation for this line.

y-5=-1(x+5)

Distr

Distribute (-1)

y-5=(-1)x+(-1)5

MultPropNegOne

Multiplication Property of -1

y-5=- x+(-5)

AddNeg

a+(- b)=a-b

y-5=- x-5

AddEqn

LHS+5=RHS+5

y-5+5=- x-5+5

AddTerms

Add terms

y=- x