To determine by what number Rahul can multiply the equation \( y = \frac{23}{3}x + 14 \) in order to clear the fractions and rewrite it in standard form, we first notice that the term \( \frac{23}{3} \) has a denominator of 3.
To eliminate the fraction, he should multiply the entire equation by the least common multiple (LCM) of the denominators present. In this case, multiply by 3:
- Multiply both sides of the equation by 3:
\[ 3y = 23x + 42 \]
This clears the fraction from the slope.
Thus, the answer is 3.