Question

1. identify the valid ( y )-intercept from the equation ( 3x + 6y = 12 ).

a. ( (0,1) )
b. ( (0,2) )
c. ( (0,3) )
d. ( (4,0) )

Explanation:

Step1: Recall y-intercept definition

The y-intercept of a line is the point where \( x = 0 \). So we substitute \( x = 0 \) into the equation \( 3x + 6y = 12 \).

Step2: Substitute \( x = 0 \)

Substituting \( x = 0 \) gives \( 3(0) + 6y = 12 \), which simplifies to \( 0 + 6y = 12 \) or \( 6y = 12 \).

Step3: Solve for y

Divide both sides by 6: \( y=\frac{12}{6}=2 \). So the y-intercept is \( (0, 2) \).

Answer:

b. \( (0, 2) \)