Applied Mathematics for Business and Economics

Lecture Note Function

The Slope of a Line

The slope of the nonvertical line passing thruough the points

()xy 11 , and ( )x2 2,y is given by the formula

21

21

Slope

y yy

x xx

Δ −

==

Δ −

y

Example 1
Find the slope of the line joining the points(−2, 5 and 3, 1) ( − ).

3.2 Horizontal and Vertical Lines ...................................................................

The horizontal line has the equationyb= , where b is a constant. Its

slope is equal to zero. The vertical line has the equationx=c, where
c is a constant. Its slope is undefined. See the figure.

3.3 The Slope-Intercept Form .........................................................................

The Slope-Intercept Form of the Equation of a Line

The equation

ymxb= +

is the equation of the line whose slope is m and whose y intercept

is the point()0,b

Example 2
Find the slope and y intercept of the line 32 yx+ = 6 and draw the graph.

3.4 The Point-Slope Form ...............................................................................

The Point-Slope Form of the Equaiton of a Line

The equation yy−= − 00 mx x( )is and equation of the line that

passes through the point (xy 00 , )and that slope equal to m.

Example 3
Find an equation of the line that passes through the point (5,1)and

whose slope is equal to1/2.

Example 4
Find an equation of the line that passes through the points(3, 2 and 1, 6− )().

•

•

(x 22 ,y)

( ) yy y^21 −

11 ,

=Δ

21

x y

x−xx=Δ

x

y

y x=c

• x

(0,b) yb=

Horizontal line

(c,0)• x

Vertical line