Beginning Algebra, 11th Edition

Finding Slopes from Equations

Find the slope of each line.

(a)

Step 1 Solve the equation for y.

Subtract from each side.

Divide by.

Slope

Step 2 The slope is given by the coefficient of x, so the slope is^25.

y= - 5

2

5

x-

4

5

- 5 y=- 2 x+ 4 2 x

2 x- 5 y= 4

2 x- 5 y= 4

EXAMPLE 5

204 CHAPTER 3 Linear Equations and Inequalities in Two Variables; Functions

NOW TRY
EXERCISE 5
Find the slope of the line.

3 x+ 5 y=- 1

Isolate yon

one side.

(b)

Subtract 8x.

Divide by 4.

The slope of this line is given by the coefficient of x, which is - 2. NOW TRY

y= - 2 x+

1

4

4 y=- 8 x+ 1

8 x+ 4 y= 1

Solve for y.

NOTE We can solve the equation (with ) for yto show that, in

general, the slope of the line is m=-AB.

Ax+By=C BZ 0

OBJECTIVE 3 Use slopes to determine whether two lines are parallel,

perpendicular, or neither. Two lines in a plane that never intersect are parallel.

We use slopes to tell whether two lines are parallel.

FIGURE 27on the next page shows the graphs of and

These lines appear to be parallel. We solve each equation for yto find the slope.

Subtract x. Subtract x.

Divide by 2. Divide by 2.

Slope Slope

• x
  2 =
  
  
  • 1 x
    2 =-
  
  
  
  

1

y= - 2 x

1

2

y =- - 2 x=- 21 x=-^12 x x- 3

1

2

x+ 2

y=

- x

2

y= - 3

- x

2

+ 2

2 y=-x+ 4 2 y=-x- 6

x+ 2 y= 4 x + 2 y=- 6

x+ 2 y= 4 x+ 2 y=-6.

Both lines have slope -^12 .Nonvertical parallel lines always have equal slopes.

The slope is

not -x 2.

-^12 ,

NOW TRY ANSWER

5. -^35

Finding the Slope of a Line from Its Equation

Step 1 Solve the equation for y.

Step 2 The slope is given by the coefficient of x.

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