Math Problem Statement
how to graph
Solution
Here's how to graph the line :
Step 1: Identify the slope and y-intercept
The equation is in slope-intercept form: , where:
- is the slope, and
- is the y-intercept (the point where the line crosses the y-axis).
For :
- The slope ,
- The y-intercept .
Step 2: Plot the y-intercept
The y-intercept is , so the line crosses the y-axis at the point . Start by plotting this point on the graph.
Step 3: Use the slope to find another point
The slope means that for every 1 unit you move to the right on the x-axis, the line falls by 2 units on the y-axis. Starting from the point :
- Move 1 unit to the right (to ),
- Move 2 units down (to ).
Plot this second point at .
Step 4: Draw the line
Now that you have two points and , draw a straight line passing through these points. This is the graph of the line .
Step 5: Extend the line
Continue the line in both directions (left and right) using the same slope. Make sure it extends across the graph, and label the points you used.
Example:
- Plot the point on the graph.
- From , move right by 1 unit and down by 2 units to reach .
- Draw a straight line connecting these two points and extend it.
This will give you the graph of the line .
If you need more help or details, feel free to ask!
Related Questions:
- How do you determine the x-intercept of a line?
- What is the difference between positive and negative slopes in terms of graphing?
- How do you graph vertical and horizontal lines?
- How can you graph a line using two points instead of slope-intercept form?
- What are some strategies for accurately graphing lines without gridlines?
Tip:
When graphing, always start with the y-intercept, and then use the slope to find additional points. This helps ensure your line is accurate.
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Math Problem Analysis
Mathematical Concepts
Graphing
Linear Equations
Slope-Intercept Form
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9