Exercise 4 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. (- 2,5) 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 ( - 2,5) & ( 1,- 1)

m=- 1- 5/1-( - 2)

▼

Calculate m

SubNeg

a-(- b)=a+b

m=- 1-5/1+2

AddSubTerms

Add and subtract terms

m=- 6/3

CalcQuot

Calculate quotient

m=- 2

Now that we know that the slope of the line is - 2, 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, 5).

y-y_1=m(x-x_1)

SubstituteValues

Substitute values

y- 5= -2 (x-( - 2))

SubNeg

a-(- b)=a+b

y-5=- 2(x+2)

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!