Question
- Bodie drew a triangle. The base of his
triangle is
the height of the triangle.
Let
height.
Let
base.
Graph
.
triangle is
Let
Let
Graph
Ask by Ryan Turner. in the United States
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
To graph the equation
, plot points where the base
is half the height
. For example, when
,
. Draw a straight line through these points to represent the relationship between the base and height of the triangle.
Solution
Certainly! Let’s graph the equation
, where:
-
represents the height of the triangle. -
represents the base of the triangle.
Understanding the Equation
The equation
shows a linear relationship between the base and the height of the triangle. For every unit increase in height, the base increases by half a unit.
Steps to Graph
-
Choose a Coordinate System:
- Horizontal Axis (X-axis): Base (
) - Vertical Axis (Y-axis): Height (
)
- Horizontal Axis (X-axis): Base (
-
Create a Table of Values:
Height ( ) Base ( ) 0 0 2 1 4 2 6 3 8 4 10 5 -
Plot the Points:
(Base) (Height) 0 0 1 2 2 4 3 6 4 8 5 10 -
Draw the Line:
- Connect the plotted points with a straight line.
- Extend the line in both directions for a complete graph.
Visual Representation
Here’s a simplified ASCII representation of the graph:
Height (h)
|
10 | *
9 |
8 | *
7 |
6 | *
5 |
4 | *
3 |
2 | *
1 |
0 |_______________________________ Base (b)
0 1 2 3 4 5
- Each
*
represents a plotted point from the table. - The line connecting these points illustrates the relationship
.
Graph Interpretation
- Slope: The slope of the line is
, indicating that for every increase of 2 units in height, the base increases by 1 unit. - Intercept: The graph passes through the origin (0,0), meaning when the height is 0, the base is also 0.
Practical Example
Suppose you have a triangle with a height of 6 units:
On the graph, this corresponds to the point (3, 6), which lies on the line
.
Using Graphing Tools
For a more precise graph, you can use graphing tools or software such as:
- Desmos: https://www.desmos.com/calculator
- GeoGebra: https://www.geogebra.org/graphing
- Microsoft Excel or Google Sheets: Utilize their charting features to plot the points and draw the line.
Conclusion
Graphing
provides a clear visual representation of how the base and height of Bodie’s triangle are related. By understanding this relationship, you can easily determine one dimension when the other is known.
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The Deep Dive
To graph the equation
, start by recognizing that this represents a linear relationship where the base
is half of the height
. You can plot points by choosing values for
:
- If
, then . - If
, then . - If
, then . - If
, then .
Plot these points on a coordinate system where the x-axis represents the height
and the y-axis represents the base
. Connect the points to create a straight line that passes through the origin, indicative of the fact that as the height increases, so does the base proportionally.
This visual representation can help in understanding the relationship between the height and the base of Bodie’s triangle, showcasing linear growth!