The equation of a line is given below. \[ 6 x+3 y=-18 \] Find the \( x \)-intercept and the \( y \)-intercept. Then use them to graph the line.
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To find the \( x \)-intercept of the line represented by the equation \( 6x + 3y = -18 \), you set \( y = 0 \). This reduces the equation to \( 6x = -18\), leading to \( x = -3 \). For the \( y \)-intercept, set \( x = 0\), giving \( 3y = -18 \) or \( y = -6 \). Thus, the intercepts are \( (-3, 0) \) for the \( x \)-intercept and \( (0, -6) \) for the \( y \)-intercept. To graph the line, plot the two intercepts: \( (-3, 0) \) on the \( x \)-axis and \( (0, -6) \) on the \( y \)-axis. Draw a straight line through these points to represent the equation \( 6x + 3y = -18 \). Voilà! You've got your line!