Graphing a line given its slope and \( y \)-intercept Graph the line with slope \( \frac{1}{3} \) and \( y \)-intercept -8 .

To graph a line with a slope of \( \frac{1}{3} \) and a \( y \)-intercept of -8, start by plotting the \( y \)-intercept on the graph at the point (0, -8). From this point, use the slope to find another point on the line. The slope \( \frac{1}{3} \) means that for every 3 units you move to the right (increasing \( x \)), you move 1 unit up (increasing \( y \)). So, from (0, -8), move right to (3, -7) and plot that point. Now draw a straight line through these points, and you’ve got your graph! For clarity, remember that the slope represents the rise over run. A common mistake when graphing is to confuse which direction to move. If you follow the slope of \( \frac{1}{3} \), it means going up (rise) for every 3 units you go across (run). Always check your calculations by picking additional points using the linear equation format \( y = mx + b \) to ensure your line is accurate!