Rahul is presented with the equation of a line in slope-intercept form: y=23x+14 . By what number can he multiply the equation in order to clear the fractions and rewrite the equation in standard form?(1 point)

Question

Responses

6
6

4
4

12
12

3

Answer 1

To rewrite the equation \( y = \frac{23}{12}x + \frac{14}{12} \) in standard form (which is \( Ax + By = C \) where A, B, and C are integers), we need to clear the fractions.

The current equation in slope-intercept form can also be expressed as:

\[ 12y = 23x + 14 \]

To eliminate the fractions in \( \frac{23}{12} \) and \( \frac{14}{12} \), we can multiply the entire equation by 12.

Thus, multiplying the original equation by 12 gives:

\[ 12y = 23x + 14 \]

or rearranging it gives:

\[ -23x + 12y = 14 \]

Therefore, the number Rahul can multiply the equation by to clear the fractions is 12.