The equation of a line is given below. \[ 3 x+y=-1 \] Find the slope and the \( y \)-intercept. Then use them to graph the line.

To find the slope and the \( y \)-intercept from the equation \( 3x + y = -1 \), we can rearrange it into slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept. Rearranging: \[ y = -3x - 1 \] From this form, we can see that the slope \( m \) is \( -3 \) and the \( y \)-intercept \( b \) is \( -1 \). This means the line crosses the \( y \)-axis at the point \( (0, -1) \) and slopes downwards as \( x \) increases. To graph the line, start at the \( y \)-intercept (0, -1) on the coordinate plane. From that point, use the slope of -3 (which means down 3 units for every 1 unit moved to the right) to plot another point. Connect these points with a straight line, and you’ll have your graph! To polish your trigonometric skills, consider diving deeper into understanding how slope can affect other types of functions—like quadratic or exponential! Trying different equations will illuminate this relationship further. Also, don’t forget to play around with graphing tools online. They can let you visualize lines, different slopes, and intercepts interactively. This fun trial-and-error approach can deepen your understanding of how changes in slope create entirely new lines!