Math Problem Statement

Use the intercepts to graph the equation x - 2y = 4.

Solution

To graph the line x2y=4x - 2y = 4 using intercepts, let's find the x-intercept and y-intercept.

Steps to Solve:

  1. Find the x-intercept: Set y=0y = 0 in the equation and solve for xx. x2(0)=4x=4x - 2(0) = 4 \Rightarrow x = 4 So, the x-intercept is (4,0)(4, 0).

  2. Find the y-intercept: Set x=0x = 0 in the equation and solve for yy. 02y=4y=20 - 2y = 4 \Rightarrow y = -2 So, the y-intercept is (0,2)(0, -2).

Plotting the Line:

  • Mark the points (4,0)(4, 0) on the x-axis and (0,2)(0, -2) on the y-axis.
  • Draw a straight line passing through these two points.

This line represents the equation x2y=4x - 2y = 4.

Would you like additional steps or a detailed explanation of the intercept method?

Here are some related questions you might find helpful:

  1. How do you find intercepts for equations in standard form?
  2. What is the slope of the line x2y=4x - 2y = 4?
  3. How can you convert x2y=4x - 2y = 4 into slope-intercept form?
  4. How would you graph a line using a different method, like plotting points?
  5. What does it mean for two lines to be parallel in terms of their equations?

Tip: Always check if your line passes through both intercept points to ensure accuracy.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Intercepts

Formulas

x-intercept: set y = 0, then solve for x
y-intercept: set x = 0, then solve for y

Theorems

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Suitable Grade Level

Grades 8-10