Objective # 6
Finding the slope of a line
Material:
page 117 to 121
Homework:
worksheet
NOTE: When we say line ... we mean straight line!
Slope of a line:
It is a number that represents the slant of a line and is represented by the
letter “m”.
“Rise” between two points on a line: It is the vertical distance between those points
“Run”between two points on a line: It is the horizontal distance between those points.
How do find the slope of a line?
Example:
Plot the following two points on a graph and draw the line that passes through those
two points. Find the rise, run and slope of that line.
(6, 9) and
(1, 2)
How can we find the rise just by looking at the coordinates?
How can we find the run just by looking at the coordinates?
Slope Formula:
Example:
Let
and
be any two points on a
Plot the following pairs of points on separate graphs, draw the line that passes
through the and find the slope of the line.
a)
(3, 9) and (-2, -3)
b)
(-1, 5) and (3, - 4)
c)
(-2, 6) and a y-intercept of -3
d)
(2, -1) and an x-intercept of 5
y-intercept:
It is the point where a line cuts the y-axis. Example:
if the y-intercept is -3
then (0-3) is the point
x-intercept:
It is the point where a line cuts the x-axis. Example:
if the x-intercept is 5
then (5, 0) is the point.
Example:
Go to page 120, reproduce the graph for # 6, 7 and calculate the slopes of each line!
Finding the slope of a line - knowing two points on the line
Worksheet
Find the slope of the line that passes through each of the following pairs of points:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
Finding the Slope of a Line
Worksheet
1.
Plot the following pairs of points on separate graphs, draw the line that passes through them and
calculate the slope using the slope formula.
2.
a)
(-3, 6) and
(4, 1)
b)
(5, 7) and (2, 1)
c)
(3, -5) and
(-2, 4)
d)
(- 4, -5) and (6, -1)
e)
(4, 6) and (4, - 2)
f)
(3, 4) and (- 2, 4)
g)
(-3, 7) and a y-intercept of 1
h)
(2, 7) and an x-intercept of - 3
Study the graphs of the following lines, pay close attention to the scales of both the x and y-axis and
calculate the slopes of each using the slope formula.
a)
b)
c)
d)
Finding the slope of a line
Worksheet
Activity # 1:
Plot the following pairs of points on the graph to their right, draw the line hat passes through those points
and use the slope formula to calculate the slope of the line.
a)
(2, 1)
(5, 8)
b)
(-2, -5)
(3, 4)
c)
(6, 3)
(- 4, 1)
d)
(2, -7)
e)
(-6,0)
(-3, 4)
f)
(0,-2)
(4, -2)
(1,5)
Which of the following best describes the above six lines? Circle the correct answer!
A. positive
1.
The sign of the slopes of each of the six lines above is:
2.
The slant of each of the six lines above is best describe as:
A. Slanting upward to the right.
OR
OR
B. negative
B. Slanting downward to the right.
Conclusion:
Lines that have a slope that is __________ always slant __________________________________________
Page -2Activity # 2:
Plot the following pairs of points on the graph to their right, draw the line hat passes through those points and
use the slope formula to calculate the slope of the line.
a)
(-2, 1)
(-5, 8)
b)
(2, -5)
c)
(-6, 3)
( 4, 1)
d)
(-2, -7)
e)
(6,0)
(-3, 4)
f)
(0,-2)
(-3, 4)
(-4, -2)
(-1,5)
Which of the following best describes the above six lines? Circle the correct answer!
A. positive
1.
The sign of the slopes of each of the six lines above is:
2.
The slant of each of the six lines above is best describe as:
A. Slanting upward to the right.
OR
OR
B. negative
B. Slanting downward to the right.
Conclusion:
Lines that have a slope that is __________ always slant __________________________________________
Page -3Activity # 3:
Plot the following pairs of points on the graph to their right, draw the line hat passes through those points and
use the slope formula to calculate the slope of the line.
a)
(2, 1)
(5, 1)
c)
(6, 3)
(- 4, 3)
e)
(-6,0)
(-3, 0)
b)
(-2, -5)
(3, -5)
d)
(2, -7)
(4, -7)
f)
(0,-2)
(-2,-2)
Which of the following best describes the above six lines? Circle the correct answer!
A. zero
1.
The slopes of each of the six lines above is:
2.
The slant of each of the six lines above is best describe as:
A. a horizontal line
OR
B. a vertical line
OR
B. undefined
Conclusion:
Lines that have a slope that is
______ always have a slant that is a _______________________________.
Page -4Activity # 4:
Plot the following pairs of points on the graph to their right, draw the line hat passes through those points and
use the slope formula to calculate the slope of the line.
a)
(2, 1)
(2, 6)
b)
(-2, -5)
(-2, 3)
c)
(6, 3)
(6, -3)
d)
(-5, -7)
(-5, -1)
e)
(-6,0)
(-6, 4)
f)
(0,-2)
(0, 6)
Which of the following best describes the above six lines? Circle the correct answer!
A. zero
1.
The slopes of each of the six lines above is:
2.
The slant of each of the six lines above is best describe as:
A. a horizontal line
OR
B. a vertical line
OR
B. undefined
Conclusion:
Lines that have a slope that is
______ always have a slant that is a _______________________________.