Exercise 19 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. (1,2) and (-2,-1) To determine the slope of the line, we use the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

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

m=-1- 2/-2- 1

SubTerms

Subtract terms

m=-3/-3

DivNegNeg

- a/- b=a/b

m=3/3

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 ( 1, 2).

y-y_1=m(x-x_1)

SubstituteValues

Substitute values

y- 2= 1(x- 1)

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-2=1(x-1)

Distr

Distribute 1

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

IdPropMult

Identity Property of Multiplication

y-2=x-1

AddEqn

LHS+2=RHS+2

y-2+2=x-1+2

AddTerms

Add terms

y=x+1