Exercise 16 Page 183

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. (-2,3) and (2,7) To determine the slope of the line, we use the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( -2,3) & ( 2,7)

m=7- 3/2-( -2)

▼

Simplify right-hand side

SubNeg

a-(- b)=a+b

m=7-3/2+2

AddSubTerms

Add and subtract terms

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 ( -2, 3).

y-y_1=m(x-x_1)

SubstituteValues

Substitute values

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

SubNeg

a-(- b)=a+b

y-3=1(x+2)

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-3=1(x+2)

Distr

Distribute 1

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

IdPropMult

Identity Property of Multiplication

y-3=x+2

AddEqn

LHS+3=RHS+3

y-3+3=x+2+3

AddTerms

Add terms

y=x+5