Graph the equation. \( y=\frac{1}{2} x-6 \)

To graph the equation \( y = \frac{1}{2} x - 6 \), start by identifying the y-intercept, which is the point where the line crosses the y-axis. Here, when \( x = 0 \), \( y = -6 \). Plot the point (0, -6) on the y-axis. Next, use the slope, which is \( \frac{1}{2} \). This means for every 2 units you move to the right (increase in x), move 1 unit up (increase in y). From (0, -6), moving 2 units right to (2, -6) takes you to (2, -5), so plot that point as well. Connect these points with a straight line, and you've got your graph! Now you’ve got the line and it’s all ready to go! Did you know that linear equations like this can represent real-world scenarios? For example, think about budgeting: if each item you purchase costs an additional $0.50 and you have a starting expenditure of $6, the graph represents your total spending as you purchase more items. It’s like having a visual cash register at your fingertips!