3.3: Graph Using Intercepts
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- Identify and find
- and -intercepts of a graph. - Graph a line using
- and -intercepts
Definition of - and -intercepts
The
The
These points have the form
Figure
To find the
Find the
Solution:
To find the
Therefore, the
Hence the
Answer:
Find the
Solution:
Begin by finding the
The
The
Answer:
Keep in mind that the intercepts are ordered pairs and not numbers. In other words, the
Figure
The horizontal line graphed above has a
Figure
The vertical line graphed above has an
Find the
- Answer
-
-intercept: ; -intercept:
Graphing Lines Using Intercepts
Since two points determine a line, we can use the
Graph using intercepts:
Solution:
Step 1: Find the
Step 2: Plot the intercepts and draw the line through them. Use a straightedge to create a nice straight line. Add an arrow on either end to indicate that the line continues indefinitely in either direction.
Answer:
Figure
Graph using intercepts:
Solution:
Begin by determining the
Next, graph the two points and draw a line through them with a straighedge.
Answer:
Figure
Graph using intercepts:
Solution:
Here the
Figure
Use the ordered pair solutions
Answer:
Figure
To summarize, any linear equation can be graphed by finding two points and connecting them with a line drawn with a straightedge. Two important and useful points are the
Graph using intercepts:
- Answer
-
-intercept: ; -intercept:
Finding Intercepts Given the Graph
The
Find the
Figure
Solution:
We see that the graph intersects the
Answer:
In our study of algebra, we will see that some graphs have many intercepts. Also, we will see that some graphs do not have any.
Given the following graph, find the
Figure
Solution:
This is a graph of a circle; we can see that it does not intersect either axis. Therefore, this graph does not have any intercepts.
Answer:
None
Key Takeaways
- Since two points determine any line, we can graph lines using the
- and -intercepts. - To find the
-intercept, set and solve for . - To find the
-intercept, set and solve for . - This method of finding
- and -intercepts will be used throughout our study of algebra because it works for any equation. - To graph a line, find the intercepts, if they exist, and draw a straight line through them. Use a straightedge to create the line and include arrows on either end to indicate that the line extends infinitely in either direction.
- Horizontal and vertical lines do not always have both
- and -intercepts.
Given the graph, find the
1.
Figure
2.
Figure
3.
Figure
4.
Figure
5.
Figure
6.
Figure
- Answer
-
1.
-intercept: ; -intercept:3.
-intercept: ; -intercept: none5.
-intercept: ; -intercept:
Find the
- Answer
-
1.
-intercept: ; -intercept:3.
-intercept: ; -intercept:5.
-intercept: ; -intercept:7.
-intercept: ; -intercept:9.
-intercept: none; -intercept:11.
-intercept: ; -intercept: none13.
-intercept: ; -intercept:
Find the intercepts and graph them.
- Answer
-
1.
Figure
3.
Figure
5.
Figure
7.
Figure
9.
Figure
11.
Figure
13.
Figure
15.
Figure
17.
Figure
19.
Figure
21.
Figure
23.
Figure
25.
Figure
27.
Figure
29.
Figure
31.
Figure
33.
Figure
Given the graph find the
1.
Figure
2.
Figure
3.
Figure
4.
Figure
5.
Figure
6.
Figure
7.
Figure
8.
Figure
9.
Figure
10.
Figure
- Answer
-
1.
-intercepts: ; -intercept:3.
-intercepts: ; -intercept:5.
-intercepts: ; -intercept:7.
-intercepts: ; -intercept:9.
-intercepts: ; -intercepts:
- What are the
-intercepts of the line ? - What are the
-intercepts of the line ? - Do all lines have intercepts?
- How many intercepts can a circle have? Draw circles showing all possible numbers of intercepts.
- Research and post the definitions of line segment, ray, and line. Why are the arrows important?
- Answer
-
1. Answers may vary
3. Answers may vary
5. Answers may vary