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Finding the Slope of a Line Worksheet

Finding the Slope of a Line Worksheet
  • Page 1
 1.  
Find the slope of the line that passes through the points (- 3, 4) and (5, 7).
a.
3 8
b.
3 2
c.
8 3
d.
2 11


Solution:

m = y2-y1x2-x1
Slope of a line passing through two points, m = Difference between the y-coordinatesDifference between the x-coordinates
[Formula.]

= (7-4)(5-(-3))
[Substitute (x1, y1) = (- 3, 4) and (x2, y2) = (5, 7).]

= 38
[Simplify the fraction.]

The slope of the line passing through the points is 3 / 8.


Correct answer : (1)
 2.  
The slope of the line in the graph is

a.
negative
b.
positive
c.
zero
d.
undefined


Solution:

The line in the graph is rising from left to right.

The line with a positive slope rises from left to right.

So, the slope of the line in the graph is positive.


Correct answer : (2)
 3.  
The slope of the line in the graph is


a.
negative
b.
positive
c.
undefined
d.
zero


Solution:

The line in the graph is falling from left to right.

The line with a negative slope falls from left to right.

So, the slope of the line in the graph is negative.


Correct answer : (1)
 4.  
The slope of the line in the graph is

a.
undefined
b.
negative
c.
positive
d.
zero


Solution:

The line in the graph is horizontal.

Slope = rise / run. The rise in the line is zero.

So, the slope of the line in the graph is zero.


Correct answer : (4)
 5.  
The slope of the line in the graph is

a.
1
b.
undefined
c.
zero
d.
- 2


Solution:

The line in the graph is vertical.

Slope = rise / run . The run is zero in the graph.

So, the slope of the line in the graph is undefined.


Correct answer : (2)
 6.  
Find the slope of the line AB in the graph.

a.
- 1
b.
1
c.
- 2


Solution:

The coordinates of the point A are (0, 2) and coordinates of the point B are (- 2, 0).

Slope = Change in yChange in x
[Formula.]

= 2 - 00 - (- 2)
[Substitute values.]

= 22 = 1
[Simplify.]

The slope of the line AB is 1.


Correct answer : (2)
 7.  
Find the slope of the line AB in the graph.


a.
2
b.
- 1
c.
1
d.
- 2


Solution:

The coordinates of point A are (- 1, 0) and coordinates of point B are (0, - 2).

Slope = Change in yChange in x = - 2 / 1

The slope of the line is - 2.


Correct answer : (4)
 8.  
What is the slope of the diameter AB of the circle shown in the graph?

a.
- 2
b.
1
c.
- 1


Solution:

Let A(2, 2) be (x1, y1) and B(- 2, - 2) be (x2, y2).

Let m be the slope of the diameter.

m = y2-y1x2-x1

m = (-2-2)(-2-2)
[Substitute the values of x1, y1, x2 and y2.]

m = 1
[Simplify the fraction.]

The slope of the diameter AB is 1.


Correct answer : (2)
 9.  
Find the slope of the line that passes through the points (13, 14) and (- 15, 17).
a.
3 28
b.
- 3 28
c.
3 29
d.
4 29


Solution:

m = y2-y1x2-x1
[Slope formula.]

= (17-14)(-15-13)
[Substitute (x1, y1) = (13, 14) and (x2, y2) = (- 15, 17).]

= - 328
[Simplify the fraction.]

The slope of the line passing through the points is - 3 / 28.


Correct answer : (2)
 10.  
Which word describes the slope of a vertical line?
a.
positive
b.
zero
c.
negative
d.
undefined


Solution:

The slope of a line is the ratio of the vertical rise to the horizontal run between any two points on the line.

Slope = Vertical riseHorizonatal run = Change in yChange in x = Change in yzero
[For a vertical line, Change in x is zero.]

The slope of the vertical line is undefined.
[Division by zero is undefined.]


Correct answer : (4)

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