Question

Rahul is presented with the equation of a line in 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 from the equation \( y = \frac{2}{3}x + \frac{1}{4} \), Rahul needs to multiply the entire equation by a number that is a common multiple of the denominators of the fractions present in the equation.

The denominators in the equation are 3 and 4. The least common multiple (LCM) of 3 and 4 is 12. Therefore, Rahul can multiply the entire equation by 12 to eliminate the fractions.

Let's multiply the equation by 12:

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

Calculating each term gives:

\[
12y = 8x + 3
\]

Thus, the rewritten equation is:

\[
8x - 12y + 3 = 0
\]

So, to clear the fractions and rewrite the equation in standard form, Rahul should multiply by **12**.