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1234Linear relations

Exercises

Exercise 1

For each of the following equations, draw the graph and determine the gradient (if possible):

a

-2 x + 3 y = 6

b

6 x - 2 y = 24

c

y = 2 x + 1

d

4 x + y = 10

e

20 x = 45

f

y + 2 = 0

Exercise 2

Given the lines l : 2 x - 4 y = -3 and m : 5 x + 4 y = 8 .

a

Algebraically determine for each line the intersects with both axes.

b

Use your graphic calculator to plot both graphs in the same window.

c

Determine the coordinates of the point of intersection of the two graphs (rounded to two decimals).

Exercise 3

You have to buy drinks for a group of 180 people. To do so, you are going to buy 1-litre packs of apple juice and orange juice. You need 90 packs, and you have a budget of € 100. Apple juice costs € 0.90 per litre and orange juice costs € 1.05 per litre. Use a for the number of packs of apple juice and s for the number of packs of orange juice.

a

What are the two equations that these variables have to solve?

b

Use your graphic calculator to plot both graphs in the same window.

c

Both variables can only take on whole numbers as values. Which solution do you find if you want to be left with as little money as possible?

Exercise 4

The following puzzle is credited to Euclid (about 300 B.C.).

A donkey and a mule are walking alongside each other, both heavily loaded with bags. The donkey moans and sighs, straining under his load, whereupon the mule says to him: What are you complaining about!? I would be carrying twice as much as you if I took one of your bags, whereas if I gave you one of my bags we would each be carrying the same amount. How many bags does each animal carry?

Solve the puzzle.

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