Question

Use the following information. Your school drama club is putting on a play next month. By selling tickets for the play, the club hopes to raise \(\$ 600\) for the drama fund for new costumes, scripts, and scenery for future plays. Let \(x\) represent the number of adult tickets they sell at \(\$ 8\) each, and let \(y\) represent the number of student tickets they sell at \(\$ 5\) each. Graph the linear function \(8 x+5 y=600\)

Short answer

The linear function \(y = 120 - 1.6x\) can be graphed starting from the y-intercept (0, 120) and plotting a line with slope -1.6. The line represents possible combinations of adult and student tickets that could be sold to reach the fundraising goal.

Step-by-step solution

Rewrite the equation

The equation must be rewritten in y = mx + b form. That is, isolate y. To do so, subtract 8x from both sides of the equation \(8 x+5 y = 600\), which gives us \(5y = 600 - 8x\). Then, divide all quantities by 5, so we obtain the equation: \(y = 120 - 1.6x\). So m (slope) = -1.6 and b (y-intercept) = 120.

Graph the linear function

Start by plotting the y-intercept (0, 120) on the graph. Since the slope is -1.6, this means that for every 1 unit increase in x, y will decrease by 1.6 units. Using this concept, plot a second point by moving 1 unit to the right and 1.6 units down from the y-intercept. Draw a line through these points to represent the linear function.

Interpret the graph

The x-intercept of the line, the point where y=0, represents the number of adult tickets that could be sold to reach the goal if no student tickets were sold. The y-intercept, where x=0, represents the number of student tickets that could be sold to reach the goal if no adult tickets were sold. Any point on the line represents possible combinations of adult and student tickets that would reach the goal.