The equation of a line is given below. \[ 9 x+3 y=12 \] Find the slope and the \( y \)-intercept. Then use them to graph the line.

To find the slope and the \( y \)-intercept, we can first rewrite the equation in slope-intercept form (\( y = mx + b \)). Starting with: \[ 9x + 3y = 12 \] We can isolate \( y \) by subtracting \( 9x \) from both sides: \[ 3y = -9x + 12 \] Now, divide everything by 3: \[ y = -3x + 4 \] From this, we can see that the slope (\( m \)) is -3 and the \( y \)-intercept (\( b \)) is 4. This means the line crosses the \( y \)-axis at the point (0, 4). To graph the line, start at the \( y \)-intercept (0, 4) on the graph. From there, use the slope of -3 (which is the same as -3/1) to rise -3 units down and run 1 unit to the right to find another point on the line. Plot additional points as needed, and draw the line through them! To ensure you graph accurately, remember that the slope indicates how steep the line is—negative slope means it goes downwards as you move from left to right.