Question

which of the following equations represents a line that has the same y-intercept as ( 3x + 6y = 12 )?

a. ( 6x + 12y = 24 )
b. ( 3x - 6y = 12 )
c. ( x + 3y = 4 )
d. ( 3x + 6y = 14 )

Explanation:

Step1: Find y-intercept of \(3x + 6y = 12\)

To find the y-intercept, set \(x = 0\):
\(3(0) + 6y = 12\)
\(6y = 12\)
\(y = \frac{12}{6} = 2\). So y-intercept is \(2\).

Step2: Find y-intercept of option a (\(6x + 12y = 24\))

Set \(x = 0\):
\(6(0) + 12y = 24\)
\(12y = 24\)
\(y = \frac{24}{12} = 2\). Y-intercept is \(2\).

Step3: Find y-intercept of option b (\(3x - 6y = 12\))

Set \(x = 0\):
\(3(0) - 6y = 12\)
\(-6y = 12\)
\(y = \frac{12}{-6} = -2\). Y-intercept is \(-2\).

Step4: Find y-intercept of option c (\(x + 3y = 4\))

Set \(x = 0\):
\(0 + 3y = 4\)
\(y = \frac{4}{3}\). Y-intercept is \(\frac{4}{3}\).

Step5: Find y-intercept of option d (\(3x + 6y = 14\))

Set \(x = 0\):
\(3(0) + 6y = 14\)
\(6y = 14\)
\(y = \frac{14}{6} = \frac{7}{3}\). Y-intercept is \(\frac{7}{3}\).

Answer:

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