Exercise 53 Page 204

An equation in slope-intercept form follows a specific format. y=mx+ b In this form, m represents the slope of the line and b represents the y-intercept. To write an equation for a line in this form, we must find the slope and the y-intercept. We will begin by finding the slope of the line that connects the given points, A(0, 3) and B(6, 0), using the Slope Formula.

m=y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( 0,3) & ( 6,0)

m=0 - 3/6- 0

SubTerms

Subtract terms

m=- 3/6

MoveNegNumToFrac

Put minus sign in front of fraction

m=-3/6

ReduceFrac

a/b=.a /3./.b /3.

m=-1/2

The slope of the line is - 12. This means, for every two units to the right we move on a coordinate plane, we move one unit down. At this point, we have the following equation. y= - 1/2x+ b To determine the value of b, we can substitute either of the given points into the equation for x and y, then solve. We will use A(0,3).

y=-1/2 x+b

SubstituteII

x= 0, y= 3

3 = -1/2( 0) + b

ZeroPropMult

Zero Property of Multiplication

3=0+b

IdPropAdd

Identity Property of Addition

3= b

RearrangeEqn

Rearrange equation

b =3

The value of b is 3. We can now write the complete equation. y = -1/2 x+ 3