Math Problem Statement

Rewrite the following equation in standard form.

y = 10x + 8

Hint: The standard form of a linear equation isAx + By = C where A and B are not both zero, and A, B, and C are integers whose GCF is 1.

Solution

To rewrite the equation y=10x+8y = 10x + 8 in standard form Ax+By=CAx + By = C, follow these steps:

  1. Subtract 10x10x from both sides of the equation to move the xx-term to the left side:

    y10x=8y - 10x = 8

  2. Rearrange the terms so that the xx-term comes before the yy-term:

    10x+y=8-10x + y = 8

Now, the equation is in standard form Ax+By=CAx + By = C, where A=10A = -10, B=1B = 1, and C=8C = 8.

Would you like further details or have any questions?

Here are 5 related questions to practice:

  1. Rewrite the equation y=3x+5y = -3x + 5 in standard form.
  2. Convert the equation 2y=4x62y = 4x - 6 to standard form.
  3. Express the equation y=23x4y = \frac{2}{3}x - 4 in standard form.
  4. What is the standard form of y=7x+1y = 7x + 1?
  5. Rewrite the equation 3y+5=2x3y + 5 = 2x in standard form.

Tip: In standard form, it's often useful to keep AA positive if possible.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Standard Form of Linear Equation

Formulas

Standard form of linear equation: Ax + By = C

Theorems

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Suitable Grade Level

Grades 7-9