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Slope Review
供稿人: Collins

Slope is defined as the steepness of a line.

Which of the following is a way to remember slope?

Run over Rise

Slow over Fast

Fast over Slow

 Rise over Run

If slope is equal to

rise over the run,

what is the slope

of the line?

-2/3

 2/3

-3/2

3/2

Rise = -3
Run =+2

If slope is equal to rise over the run,

what is the slope of the line?

Rise =+5
Run=+3

3/5

 5/3

-3/5

-5/3

Find the slope of the line.

-1/2

2

 -2

1/2

Find the slope of the line.
 0 slope

undefined slope

10

-10

Find the slope of the line.

0 slope

3

 -3

undefined slope

Find the slope

of the line.

4/3

 -4/3

3/4

-3/4

Undefined
?
Match each graph with the correct slope. Drag each.
Positive
?
Negative
?
0 Slope
?

The slope of a line can be found only given two points

as well.  If two points (x1, y1) and (x2, y2) are given,

the slope can be found using the slope formula,

which is:

 

                                


                                y2 - y1

                                x2 - x1

m =

Find the slope of the line that passes through the

two points (7, 2) and (-4, -6).

m =
x1=7, y1=2             x2 = -4, y2 = -6

y2 - y1

x2 - x1

-6-2

-4-7

=

-8       8

-11    11

=

Find the slope of the line that passes through

the points (8, 3) and (2, 9).

 

         9 - 3            6

         2 - 8           -6

=
=

Find the slope of the line that passes through the

points (7, -3) and (-4, 5).

 

 

 5 - (-3)          

 -4 - 7                  -11

=

Find the slope of the line that passes through the

two points (-2, 8) and (10, -4).

 

 

  -4 - 8          -12

10 - (-2)         12

=
=

Find the slope of the line that passes through

the points (3a - 1, a + 1) and (a + 5, 2a - 3).

 

(2a - 3) - (a + 1)     2a - 3 - a - 1       a - 4

(a + 5) - (3a - 1)     a + 5 - 3a + 1   -2a + 6

=
=

Find the slope of the line that  passes through

the points (3a - 1, a + 1) and (5a + 2, 2a + 1).

 

(2a + 1) - (a + 1)        2a + 1 - a - 1            a

(5a + 2) - (3a - 1)       5a + 2 - 3a + 1   

=
=
Remember, m/m = 1.

Find the slope of the line that passes through

the points (-3a, 7a) and (4a, 9a).

m=

Find the slope of the line that passes through

the points (8, 6) and (-3, -3).

Notice that the coordinates of a point on the x-axis

will be (#, 0), where # stands for any number.  Also

notice the coordinates of a point on the y-axis will

be (0, #), where # stands for any number.

?

(0, -2)

y-int

(3, 0)

x-int

If given an equation, you can then substitute 0 in for

x when trying to find the y-intercept and also

substitute 0 in for y when trying to find the y-intercept.

Find the x-intercept:

3x - 5(0) = 30

3x = 30

x = 10

      Given:

3x - 5y = 30

Find the y-intercept:

3(0) - 5y = 30

-5y = 30

y = -6

Find the x-intercept:

2x + 3(0) = -18

2x = -18

x =

      Given:

2x + 3y = -18

Find the y-intercept:

2(0) + 3y = -18

3y = -18

y =

Find the x-intercept

and y-intercept from the graph.

x =
y =

Find the x-intercept and y-intercept

of the given equation.

x =

     Given:

4x - 5y = 60

 

y =

When solved for y, a linear equation will be in the

form y = mx + b.  Remember, m is the slope!

What is the slope of the equation y = -4x + 8?
The slope of y = -4x + 8 is -4.
m

What is the slope of the linear equation?

 

y = 2 x - 6

The slope of y = 2 x - 6 is
m

What is the slope of the linear equation?

 

y = 3/4 x + 9

m =

Solve the equation 3x - 2y = -6 for y and then state

the slope of the line.

 

3x - 2y = -6

-3x           -3x

-2y = -3x - 6

dvide by -2

y = 3/2x + 3

 

The slope is 3/2.

Solve the equation -x + 2y = 10 for y and then

state the slope of the line.

 

-x + 2y = 10

+x            +x

2y = x + 10

Divide by 2

 y = 1/2 x + 5

 

The slope of the line is

The standard form of a linear equation is

Ax + By = C.

Change y = -4x - 7 into standard form.

 

   y = -4x - 7

+4x   +4x

 

4x + y = -7

Change the equation y = 6x - 2 into standard form.

 

    y = 6x - 2

-6x    -6x

 

-6x + y = -2

Change the equation y = 5x - 4 into standard form.

 

   y = 5x - 4

-5x   -5x

 

                 + y = -4

You are now finished with your slope tutorial.

 

Wasn't hard, was it!

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