Math Problem Statement

Find the x-intercept and the y-intercept of the line with the equation 2x - 4y = 8, and graph the line.

Solution

To find the x-intercept and y-intercept of the given line equation 2x4y=82x - 4y = 8, we will follow these steps:

Finding the x-intercept

The x-intercept occurs when y=0y = 0. Substitute y=0y = 0 into the equation and solve for xx:

2x4(0)=82x - 4(0) = 8 2x=82x = 8 x=4x = 4

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

Finding the y-intercept

The y-intercept occurs when x=0x = 0. Substitute x=0x = 0 into the equation and solve for yy:

2(0)4y=82(0) - 4y = 8 4y=8-4y = 8 y=2y = -2

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

Graphing the Line

Using the intercepts found, we can graph the line by plotting the points (4,0)(4, 0) and (0,2)(0, -2) and then drawing a straight line through these points.

Would you like a detailed graphical representation of the line, or do you have any questions about the process?

Related Questions:

  1. How do you find the slope of the line from the given equation?
  2. Can you convert the given equation to slope-intercept form y=mx+by = mx + b?
  3. What is the distance between the x-intercept and y-intercept?
  4. How would you find the x-intercept and y-intercept if the equation were in a different form, such as point-slope form?
  5. How can you check if a point lies on the line given by the equation 2x4y=82x - 4y = 8?

Tip:

When finding intercepts, remember that the x-intercept is found by setting y=0y = 0 and solving for xx, while the y-intercept is found by setting x=0x = 0 and solving for yy.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Graphing

Formulas

General form of a line: Ax + By = C
Finding x-intercept: Set y = 0
Finding y-intercept: Set x = 0

Theorems

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Suitable Grade Level

Grades 8-10