Math Problem Statement

y=3/2x+4 write in standard form

Solution

To write the equation y=32x+4y = \frac{3}{2}x + 4 in standard form, follow these steps:

Step 1: Start with the given equation

y=32x+4y = \frac{3}{2}x + 4

Step 2: Eliminate the fraction

Multiply every term by 2 to get rid of the fraction: 2y=3x+82y = 3x + 8

Step 3: Rearrange to standard form

Move all terms involving xx and yy to one side of the equation and the constant to the other side: 3x+2y=8-3x + 2y = 8

Step 4: Adjust signs if necessary

Standard form often has the xx-coefficient as positive. Multiply the entire equation by 1-1 if needed: 3x2y=83x - 2y = -8

Final Answer:

The equation in standard form is: 3x2y=83x - 2y = -8


Would you like more details or have any questions?

Related Questions:

  1. How do you convert a standard form equation back to slope-intercept form?
  2. What is the slope and y-intercept of the equation 3x2y=83x - 2y = -8?
  3. How do you graph equations in standard form?
  4. What are the characteristics of equations in standard form?
  5. Can you solve for xx or yy in this standard form equation?

Tip: Always ensure the coefficients in standard form are integers with no common factors!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Standard Form Conversion

Formulas

Standard form of a linear equation: Ax + By = C
Slope-intercept form of a linear equation: y = mx + b

Theorems

Properties of equality (used to rearrange terms and eliminate fractions)

Suitable Grade Level

Grades 8-10