Math Problem Statement

Use the intercepts to graph the equation x - 4y = 8.

Solution

To graph the equation x4y=8x - 4y = 8 using the intercepts, let's find the xx- and yy-intercepts and then plot the line through those points.

Step 1: Find the xx-intercept

The xx-intercept occurs where y=0y = 0.

  1. Substitute y=0y = 0 into the equation: x4(0)=8x - 4(0) = 8
  2. Simplify to find xx: x=8x = 8

So, the xx-intercept is at (8,0)(8, 0).

Step 2: Find the yy-intercept

The yy-intercept occurs where x=0x = 0.

  1. Substitute x=0x = 0 into the equation: 04y=80 - 4y = 8
  2. Solve for yy: 4y=8y=2-4y = 8 \Rightarrow y = -2

So, the yy-intercept is at (0,2)(0, -2).

Step 3: Plot the Intercepts and Draw the Line

On the graph:

  • Plot the point (8,0)(8, 0) on the xx-axis.
  • Plot the point (0,2)(0, -2) on the yy-axis.
  • Draw a straight line passing through these two points to represent the equation x4y=8x - 4y = 8.

Would you like additional details on how this line is derived, or any assistance with other questions?

Here are five related questions to deepen your understanding:

  1. How would you rewrite the equation x4y=8x - 4y = 8 in slope-intercept form?
  2. What would the graph look like if the equation were x+4y=8x + 4y = 8?
  3. How do you interpret the slope of the line from the equation x4y=8x - 4y = 8?
  4. How can you verify the intercepts algebraically?
  5. What would be the effect on the intercepts if the equation were 2x8y=162x - 8y = 16?

Tip: When finding intercepts, always set the opposite variable to zero, as intercepts are the points where the line crosses each axis.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Linear Equations
Intercepts
Graphing

Formulas

x-intercept: Set y = 0 in the equation
y-intercept: Set x = 0 in the equation

Theorems

-

Suitable Grade Level

Grades 9-10