Which equation represents a line with a slope of 3 and a \( y \)-intercept of \( 6 ? \) A \( 3 x-y=-6 \) B \( 3 y+x=6 \) C \( 3 x-y=6 \) (D) \( 3 y+x=-6 \)

The equation of a line in slope-intercept form is given by \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept. With a slope of \( 3 \) and a \( y \)-intercept of \( 6 \), the equation would be \( y = 3x + 6 \). To find the equivalent form among the options, it can be rearranged to get \( -3x + y = 6 \) or \( 3x - y = -6 \), leading us to option A: \( 3x - y = -6 \). A fun way to check if a line is correct is to think about where it crosses the \( y \)-axis. For a \( y \)-intercept of \( 6 \), if you plug \( x = 0 \) into your equation, does \( y \) come out as \( 6 \)? If yes, you’ve hit the bullseye! This method ensures you’re on target without wrangling with numbers too much.