Exercise 17 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. (4,1) and (8,2) To determine the slope of the line, we use the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 4,1) & ( 8,2)

m=2- 1/8- 4

SubTerms

Subtract terms

m= 1/4

Now that we know the slope of the line is 14, 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 ( 4, 1).

y-y_1=m(x-x_1)

SubstituteValues

Substitute values

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

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-1=1/4(x-4)

Distr

Distribute 1/4

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

MoveRightFacToNumOne

1/b* a = a/b

y-1=1 * x/4-1 * 4/4

IdPropMult

Identity Property of Multiplication

y-1=x/4-4/4

QuotOne

a/a=1

y-1=x/4-1

AddEqn

LHS+1=RHS+1

y-1+1=x/4-1+1

AddTerms

Add terms

y=x/4

MovePartNumRight

a* b/c=a/c* b

y=1/4x