Discuss the difference in graphing a function using intercept method vs. plotting points. Do you always have to solve for y when graphing a line? Which method do you find best to use when graphing? When looking at an equation, is there any instance where one method is more convenient than another? How different is graphing a line from graphing an inequality? What do you have to watch out for? What are the challenges you find in graphing inequalities?
Answer : (1) The intercept method (finding the x and y intercepts) works well in most cases if the intercept is a whole number or a half as you can plot these accurately but cases like 3y + 7x = 10 would be difficult to plot accurately using this method.
(2) You do not always have to solve for y in simple cases like y = 5 or x = -8 . In other cases it might be easier to solve for x:
x + 6y = 10 can easily be dealt with by re-writing it as x = 10 - 6y and choosing y =0, y =1 and finding corresponding values for x
(3) As hinted in parts(1) and (2) it depends on the actual equation of the line, but using intercept method is usually best.
(4) If the equation is given in the form y = mx +c then choose x=0 , x=1 … and work out y
or if x= by + d then choose y= 0, y =1 ...and work out x
(5) To graph an inequality, first you have to draw the corresponding line,
but you must be careful: to use dotted lines for inequalities involving less than (<) or greater than (>) and solid if it is ≤ or ≥. The solution to the inequality is an area so you have to decide which side of the line you should shade.
In the business world you have to minimize cost. You have to obey certain conditions (like customer must be 100 or more for viability) and certain restraints (distance to travel for an order must be less than 30 miles). A system of constraints involve solving a system of inequalities and then maximizing the profit or minimizing the cost.
All these involve solving inequalities, which are very important in business.
May 9th, 2015
A complicated business problem might involve 40 linear inequalities and require the use of a computer to solve.
May 9th, 2015
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