Math Problem Statement

solve

Find the x-intercept and the y-intercept of the equation 4x - 2y = 8. Then use them to graph the line.

Solution

Let's solve the equation step by step.

The given equation:

4x2y=84x - 2y = 8

Step 1: Find the x-intercept.

At the x-intercept, y=0y = 0. Substitute y=0y = 0 into the equation: 4x2(0)=8    4x=8    x=24x - 2(0) = 8 \implies 4x = 8 \implies x = 2 So, the x-intercept is: x=2or the point (2,0)x = 2 \quad \text{or the point } (2, 0)

Step 2: Find the y-intercept.

At the y-intercept, x=0x = 0. Substitute x=0x = 0 into the equation: 4(0)2y=8    2y=8    y=44(0) - 2y = 8 \implies -2y = 8 \implies y = -4 So, the y-intercept is: y=4or the point (0,4)y = -4 \quad \text{or the point } (0, -4)

Step 3: Plot the points and draw the line.

  1. Plot the x-intercept at (2,0)(2, 0).
  2. Plot the y-intercept at (0,4)(0, -4).
  3. Connect these two points with a straight line.

Final Results:

  • x-intercept: x=2x = 2
  • y-intercept: y=4y = -4

Would you like a graph or further explanation? Let me know!
Here are some related questions to expand your understanding:

  1. How do you find intercepts in a general linear equation?
  2. Can we express 4x2y=84x - 2y = 8 in slope-intercept form (y=mx+by = mx + b)?
  3. What is the slope of this line?
  4. What happens to the intercepts if the equation changes slightly, e.g., 4x2y=104x - 2y = 10?
  5. How do parallel and perpendicular lines relate to this equation?

Tip: Always verify your intercepts by substituting back into the original equation!

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Intercepts
Graphing

Formulas

x-intercept: Set y = 0 in ax + by = c
y-intercept: Set x = 0 in ax + by = c

Theorems

Intercept Definition
Linear Equation Properties

Suitable Grade Level

Grades 8-10