Questions: What is the equation in standard form of the line (y=frac19 x+5) ? A. (x=9 y-45) B. (x-9 y=-45) C. (9 y=x+45) D. (9 y-x=45)

$What is the equation in standard form of the line (y=frac19 x+5) ? A. (x=9 y-45) B. (x-9 y=-45) C. (9 y=x+45) D. (9 y-x=45)$

Transcript text: What is the equation in standard form of the line $y=\frac{1}{9} x+5$ ? A. $x=9 y-45$ B. $x-9 y=-45$ C. $9 y=x+45$ D. $9 y-x=45$

Solution

Solution Steps

To convert the given equation $ y = \frac{1}{9}x + 5 $ into standard form, we need to rearrange it into the form $ Ax + By = C $, where $ A $, $ B $, and $ C $ are integers, and $ A $ is non-negative. We can do this by eliminating the fraction and moving all terms to one side of the equation.

Step 1: Start with the Given Equation

The given equation of the line is in slope-intercept form:
\[ y = \frac{1}{9}x + 5 \]

Step 2: Eliminate the Fraction

To eliminate the fraction, multiply every term by 9:
\[ 9y = x + 45 \]

Step 3: Rearrange to Standard Form

Rearrange the equation to get all terms on one side:
\[ 9y - x = 45 \]