Questions: Write in standard form y-3=4/3(x-3)

Transcript text: Write in standard form \[ y-3=\frac{4}{3}(x-3) \]

Solution

Solution Steps

To convert the given equation from point-slope form to standard form, we need to first distribute the fraction on the right side, then move all terms to one side of the equation to set it equal to zero. Finally, we rearrange the terms to match the standard form \(Ax + By = C\).

Step 1: Rewrite the Original Equation

The original equation given in point-slope form is

\[ y - 3 = \frac{4}{3}(x - 3). \]

Step 2: Distribute the Right Side

Distributing the right side, we have:

\[ y - 3 = \frac{4}{3}x - 4. \]

Step 3: Rearrange to Standard Form

Next, we move all terms to one side to set the equation to zero:

\[ \frac{4}{3}x - y - 1 = 0. \]

Step 4: Eliminate Fractions

To express the equation in standard form \(Ax + By = C\) without fractions, we can multiply through by 3:

\[ 4x - 3y = 3. \]