Exercise 5 Page 184

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

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

SubNeg

a-(- b)=a+b

m=-1+2/2+3

AddSubTerms

Add and subtract terms

m=1/5

Now that we know the slope of the line is 15, 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)= 1/5(x-( -3))

SubNeg

a-(- b)=a+b

y+2=1/5(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!