Math Problem Statement
Solution
The equation provided in the image is:
To graph this linear equation using intercepts, let's follow these steps:
1. Find the x-intercept:
The x-intercept occurs when . Substituting into the equation:
Thus, the x-intercept is .
2. Find the y-intercept:
The y-intercept occurs when . Substituting into the equation:
Thus, the y-intercept is .
3. Plot the points:
- Plot the x-intercept on the graph.
- Plot the y-intercept on the graph.
4. Draw the line:
Using the two points and , draw a straight line through them. This line represents the graph of the equation .
Would you like a detailed explanation on how to handle any part of this, or do you have specific questions about it?
Questions for Further Exploration:
- How do we verify if a point lies on the graph of the equation?
- What is the slope of the line from the equation ?
- Can we rewrite the equation in slope-intercept form? How does it help in graphing?
- How does the graph change if the equation is altered to ?
- How do we graph equations that are not in standard linear form?
Tip:
When graphing linear equations, using both the x- and y-intercepts is a quick and efficient method to plot the line.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Graphing
Formulas
x - 2y = 4 (standard form of a linear equation)
Theorems
Intercept Theorem
Slope-Intercept Form
Suitable Grade Level
Grades 8-10