Question

which of the following equations represents a line that has the same y-intercept as $3x + 6y = 12$?
a. $3x - 6y = 12$
b. $3x + 6y = 14$
c. $x + 3y = 4$
d. $6x + 12y = 24$

Explanation:

Step1: Find y-intercept of given line

Rewrite \(3x + 6y = 12\) in slope-intercept form \(y = mx + b\):
\(6y = -3x + 12\) → \(y = -\frac{1}{2}x + 2\). So y-intercept \(b = 2\).

Step2: Check y-intercept of option a

\(3x - 6y = 12\) → \(-6y = -3x + 12\) → \(y = \frac{1}{2}x - 2\). \(b = -2\) (not 2).

Step3: Check y-intercept of option b

\(3x + 6y = 14\) → \(6y = -3x + 14\) → \(y = -\frac{1}{2}x + \frac{7}{3}\). \(b = \frac{7}{3}\) (not 2).

Step4: Check y-intercept of option c

\(x + 3y = 4\) → \(3y = -x + 4\) → \(y = -\frac{1}{3}x + \frac{4}{3}\). \(b = \frac{4}{3}\) (not 2).

Step5: Check y-intercept of option d

\(6x + 12y = 24\) → \(12y = -6x + 24\) → \(y = -\frac{1}{2}x + 2\). \(b = 2\) (matches).

Answer:

d. \(6x + 12y = 24\)