Convert the slope intercept form equation y = -2/5x intoStandard form

Convert the slope intercept form equation y = -2/5x into
Standard form.

The Correct Answer and Explanation is :

To convert the slope-intercept form equation ( y = \frac{-2}{5}x ) into standard form, we need to rearrange the equation into the format:

[
Ax + By = C
]

Where:

• ( A ), ( B ), and ( C ) are integers,
• ( A ) should be positive if possible, and
• ( A ), ( B ), and ( C ) should not have any common factors other than 1.

Step-by-step Conversion:

1. Start with the slope-intercept form equation:
   [
   y = \frac{-2}{5}x
   ]
2. Eliminate the fraction by multiplying both sides of the equation by 5. This will clear the denominator on the right-hand side:
   [
   5y = -2x
   ]
3. Rearrange the equation to get it in standard form ( Ax + By = C ). To do this, move the ( -2x ) term to the left side:
   [
   2x + 5y = 0
   ]

Now, the equation is in standard form, with ( A = 2 ), ( B = 5 ), and ( C = 0 ).

Explanation:

1. Understanding Standard Form:
   The standard form of a linear equation is ( Ax + By = C ), where ( A ), ( B ), and ( C ) are integers. The coefficient of ( x ) (represented by ( A )) is typically positive. If ( A ) is negative, the equation can be multiplied by -1 to make it positive.
2. Eliminating Fractions:
   In the original equation ( y = \frac{-2}{5}x ), there is a fraction involved. By multiplying both sides of the equation by 5, we eliminate the fraction. This ensures that all the terms in the equation are integers, which is a key requirement for standard form.
3. Rearranging:
   After clearing the fraction, the equation is rearranged to have all terms involving variables on one side and the constant on the other. The result is a linear equation in standard form.

Thus, the final standard form of the given equation is:
[
2x + 5y = 0
]