Math Problem Statement

Use intercepts and a checkpoint to graph the linear function x - 2y = 4.

Solution

The equation provided in the image is:

x2y=4x - 2y = 4

To graph this linear equation using intercepts, let's follow these steps:

1. Find the x-intercept:

The x-intercept occurs when y=0y = 0. Substituting y=0y = 0 into the equation:

x2(0)=4x=4x - 2(0) = 4 \quad \Rightarrow \quad x = 4

Thus, the x-intercept is (4,0)(4, 0).

2. Find the y-intercept:

The y-intercept occurs when x=0x = 0. Substituting x=0x = 0 into the equation:

02y=4y=20 - 2y = 4 \quad \Rightarrow \quad y = -2

Thus, the y-intercept is (0,2)(0, -2).

3. Plot the points:

  • Plot the x-intercept (4,0)(4, 0) on the graph.
  • Plot the y-intercept (0,2)(0, -2) on the graph.

4. Draw the line:

Using the two points (4,0)(4, 0) and (0,2)(0, -2), draw a straight line through them. This line represents the graph of the equation x2y=4x - 2y = 4.

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:

  1. How do we verify if a point lies on the graph of the equation?
  2. What is the slope of the line from the equation x2y=4x - 2y = 4?
  3. Can we rewrite the equation in slope-intercept form? How does it help in graphing?
  4. How does the graph change if the equation is altered to x2y=6x - 2y = 6?
  5. 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