Exercise 6 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. (1,0) and (4, 4) To determine the slope of the line, we use the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 1,0) & ( 4,4)

m=4- 0/4- 1

SubTerms

Subtract terms

m=4/3

Now that we know the slope of the line is 43, 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, 0).

y-y_1=m(x-x_1)

SubstituteValues

Substitute values

y- 0= 4/3(x- 1)

SubTerm

Subtract term

y=4/3(x-1)

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!