Intermediate Algebra (11th edition)

Finding the Slope from an Equation

Find the slope of the graph of

Solve the equation for y.

Subtract 3x.

Divide eachterm by.

The slope is given by the coefficient of x, so the slope is NOW TRY

3

5.

y= - 5

3

5

x-

8

5

- 5 y=- 3 x+ 8

3 x- 5 y= 8

3 x- 5 y=8.

EXAMPLE 4

SECTION 3.2 The Slope of a Line 151

• 3 x
  
  
  • 5 =
    
    
    • 3
    
    
    
    
  
  
  
  

- 5

x

1 =

3

5 x

OBJECTIVE 3 Graph a line, given its slope and a point on the line.

Using the Slope and a Point to Graph Lines

Graph each line described.

(a)With slope and y-intercept

Begin by plotting the point P as shown in FIGURE 18. Then use the slope

to find a second point.

We m ov e 2 units upfrom and then 3 units to the rightto locate another point

on the graph, R 1 3, - 22 .The line through P 1 0, - 42 and Ris the required graph.

1 0, - 42

m=

change in y

change in x

=

2

3

1 0, - 42 ,

1 0, - 42

2

3

EXAMPLE 5

x

y

0

–4–2

2

4

⎩Right 3⎨⎧

Up 2⎧⎨⎩

P(0, –4)

R

(^24) x
y
–4
2
4
–4–2 46
P(3, 1)
R
Right 1
Down 4
0
FIGURE 18

(b)Through with slope

Start by locating the point , as shown in FIGURE 19. Find a second point R

on the line by writing the slope as and using the slope formula.

We move 4 units downfrom and then 1 unit to the rightto locate this second

point. The line through and Ris the required graph.

The slope also could be written as

In this case, the second point Ris located 4 units upand 1 unit to the left.Verify that

this approach also produces the line in FIGURE 19.

m=

change in y

change in x

=

4

- 1

.

R 1 4, - 32 P 1 3, 1 2

1 3, 1 2

m=

change in y

change in x

=

- 4

1

• 
  

  4

  
  


• 
  

  (^41)

  
  

P 1 3, 1 2

1 3, 1 2 - 4

FIGURE 19

NOW TRY

NOW TRY
EXERCISE 4
Find the slope of the graph
of 5x- 4 y=7.

NOW TRY ANSWERS
4.
5.

5

4

NOW TRY
EXERCISE 5
Graph the line passing
through that has

slope .- (^23)

1 - 4, 1 2

0

y

x

(–1, –1)

(– 4, 1)