Auto-time, a manufacturer of 24-hour variable timers, has a monthly fixed cost of RM48,000 and a production cost of RM8 for each timer manufactured. The units sell for RM14 each.

So if they make and sell T timers, their cost is 48000+ 8T. Their income is 14T. Those are both "linear functions" so their graphs are straight lines. And straight lines are determined by two points.

When T= 0, the cost is 48000+ 8(0)= 48000. When T= 10000, the cost is 48000+ 8(10000)= 128000. Mark the points (0, 48000) and (10000, 128000) on your graph and draw the line through them. When T= 0, the income is 14(0)= 0. When T= 10000, the income is 14(10000)= 140000. Mark the points (0, 0) and (100, 140000) and draw the line between them.

The "break even point" is where there is neither profit nor loss- the cost of production is the same as the income. Where do those two lines intersect?

Algebraically, saying that cost is the same as income means that the two functions above are equal: 48000+ 8T= 14T. Solve that equation for T. You should get the same T as where the two lines intersect.

The profit is the income minus the cost: 14T- (48000+ 8T)= 14T- 8T- 48000= 6T- 48000. Again that is a straight line. When T= 0, the "profit" is 6(0)- 48000= -48000 (negative since this is actually a loss). When T= 10000 the profit is 6(10000)- 48000= 60000- 48000= 12000. Mark the points (0, -48000) and (10000, 12000) and draw the line between them. Notice that (0, -48000) is below the x-axis and (10000, 12000) is above it. A some place between T= 0 and T= 10000 that line must cross the x-axis. Of course, on the x-axis, the profit is 0- there is no profit and no loss. That is again the "break even point". To find that T set the profit equal to 0, 6T- 48000= 0, and solve for T. That will be the same as the two answers above.