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 \( y = \frac{2}{3}x + \frac{1}{4} \), we need to find a common denominator for the fractions. The denominators present in the equation are 3 and 4.

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

Let's perform the multiplication:

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

Calculating each term:

1. For \( 12\left(\frac{2}{3}x\right) \): \[ 12 \cdot \frac{2}{3} = 4 \cdot 2 = 8 \] So this term becomes \( 8x \).

2. For \( 12\left(\frac{1}{4}\right) \): \[ 12 \cdot \frac{1}{4} = 3 \] So this term becomes \( 3 \).

Thus, we rewrite the equation as:

\[ 12y = 8x + 3 \]

To have the equation in standard form (Ax + By = C), we can rearrange it as follows:

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

Now, if we multiply the entire equation by -1 for a standard positive coefficient on \( x \):

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

In conclusion, Rahul should multiply the entire equation by 12 to clear the fractions and write the equation in standard form.