Answer:
Find the Slope from a Graph
Identify rise and run from a graph
Distinguish between graphs of lines with negative and positive slopes
Find the Slope from Two Points
Use the formula for slope to define the slope of a line through two points
Find the Slope of Horizontal and Vertical Lines
Find the slope of the lines
x
=
a
and
y
=
b
Recognize that horizontal lines have slope = 0
Recognize that vertical lines have slopes that are undefined
Identify slopes of parallel and perpendicular lines
Given a line, identify the slope of another line that is parallel to it
Given a line, identify the slope of another line that is perpendicular to it
Interpret slope in equations and graphs
Verify the slope of a linear equation given a dataset
Interpret the slope of a linear equation as it applies to a real situation
Identify slope from a graph
The mathematical definition of slope is very similar to our everyday one. In math, slope is used to describe the steepness and direction of lines. By just looking at the graph of a line, you can learn some things about its slope, especially relative to other lines graphed on the same coordinate plane. Consider the graphs of the three lines shown below:
You can determine the slope of a line from its graph by looking at the rise and run. One characteristic of a line is that its slope is constant all the way along it. So, you can choose any 2 points along the graph of the line to figure out the slope. Let’s look at an example.
EXAMPLE
Use the graph to find the slope of the line.
A line that crosses the points (2,1) and (6,3). A blue line labeled Rise goes up two units from the point (2,1). A red line labeled Run goes left from the point (6,3) so that it forms a triangle with the main line and the Rise line. A formula says slope equals rise over run.
Show Solution
This line will have a slope of
1
2
no matter which two points you pick on the line. Try measuring the slope from the origin,
(
0
,
0
)
, to the point
(
6
,
3
)
. You will find that the
rise
=
3
and the
run
=
6
. The slope is
rise
run
=
3
6
=
1
2
. It is the same!
Let’s look at another example.
EXAMPLE
Use the graph to find the slope of the two lines.
A graph showing two lines with their rise and run. The first line is drawn through the points (-2,1) and (-1,5). The rise goes up from the point (-2,1) to join with the run line that goes right to the point (-1,5). The second line is drawn through the points (-1,-2) and (3,-1). The rise goes up from the point (-1,-2) to join with the run to go right to the point (3,-1).
Show Solution
When you look at the two lines, you can see that the blue line is steeper than the red line. It makes sense the value of the slope of the blue line, 4, is greater than the value of the slope of the red line,
1
4
. The greater the slope, the steeper the li
Explanation: