Rahul is presented with the equation of a line and slope intercept form y=2/3x+1/4 by what number can he multiply the equation in order to clear the fractions and rewrite the equation in standard form

Answer 1

To clear the fractions in the equation \( y = \frac{2}{3}x + \frac{1}{4} \), we can find the least common multiple (LCM) of the denominators, which are 3 and 4.

The LCM of 3 and 4 is 12. By multiplying the entire equation by 12, we can eliminate the fractions.

Let's multiply each term in the equation by 12:

\[ 12y = 12\left(\frac{2}{3}x\right) + 12\left(\frac{1}{4}\right) \]

Calculating each term:

1. \( 12y \) remains \( 12y \).
2. For \( 12 \cdot \frac{2}{3}x \): \[ 12 \cdot \frac{2}{3} = 4 \cdot 2 = 8 \Rightarrow 8x \]
3. For \( 12 \cdot \frac{1}{4} \): \[ 12 \cdot \frac{1}{4} = 3 \]

Putting it all together, we have: \[ 12y = 8x + 3 \]

Thus, if Rahul multiplies the equation by 12, the fractions will be cleared, and the equation can now be rewritten in a standard form.