Math Problem Statement

Express in the form of ax + by + c = 0: sqrt(2)x = 3sqrt(2)y + 2

Solution

The problem in the image reads:

3. Express in the form of ax+by+c=0ax + by + c = 0:

2x=32y+2\sqrt{2}x = 3\sqrt{2}y + 2

Solution:

We need to rearrange this equation into the form ax+by+c=0ax + by + c = 0, where aa, bb, and cc are constants.

Start with the given equation:

2x=32y+2\sqrt{2}x = 3\sqrt{2}y + 2

Step 1: Move all terms to one side of the equation.

Subtract 32y3\sqrt{2}y and 22 from both sides:

2x32y2=0\sqrt{2}x - 3\sqrt{2}y - 2 = 0

Step 2: The equation is now in the form ax+by+c=0ax + by + c = 0, where:

  • a=2a = \sqrt{2},
  • b=32b = -3\sqrt{2},
  • c=2c = -2.

Thus, the equation in the form ax+by+c=0ax + by + c = 0 is:

2x32y2=0\sqrt{2}x - 3\sqrt{2}y - 2 = 0

Would you like more details on any specific step or have further questions?

Here are some related questions to explore:

  1. How would the equation change if we squared both sides?
  2. What would happen if we isolated yy instead of xx?
  3. Can we simplify the equation further by factoring out 2\sqrt{2}?
  4. What is the geometric interpretation of this linear equation?
  5. How would the coefficients change if we multiplied through by 2\sqrt{2}?

Tip: Always aim to simplify equations by factoring out common terms when possible.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

ax + by + c = 0

Theorems

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Suitable Grade Level

Grades 10-12