A straight-line graph can be written in slope-intercept form, . Read where the line crosses the vertical axis, then use two labeled points to find , the change in revenue per ticket. Desmos can divide those changes for you. Read the axis values, not the number of grid boxes. An equation can have the right starting value but the wrong slope.
Hints
- Hint 1
The -intercept is where the line crosses the vertical axis, so . Its -value is the constant term in . What revenue does the graph show when no tickets have been sold?
- Hint 2
The slope measures revenue gained per additional ticket. Subtract the revenues at two labeled points, then divide by the change in tickets between those same points. What number should multiply ?
Step-by-step
Read the intercept and calculate the slope
Step 1Find the starting revenue
The line crosses the vertical axis at . That means revenue is $50 when zero tickets have been sold. In slope-intercept form , is the value when , so . The is the starting value, not the amount earned per ticket.
- Step 2
Find the revenue per ticket
The labeled points and give two changes you can compare. The slope is the change in revenue divided by the change in tickets, so type in Desmos. It prints , meaning revenue rises by $15 per ticket. Keep the point order the same in the numerator and denominator; don't count boxes on axes with different scales.
- Step 3
Write the revenue equation
Put the per-ticket increase in front of and the starting revenue after it: . This gives the total revenue, in dollars, from selling tickets. Choice A.