Linear functions: 9th grade math exercises with answers in PDF.

Linear functions: math exercises in 3rd grade corrected in PDF.

Exercise 1

Exercise 2

Exercise 3 Linear functions

Exercise 4

Exercise 5 Linear functions

Exercise 6

Exercise 7

Exercise 8

Exercise 9 linear functions

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1 Exercise 1
2 Exercise 2
3 Exercise 3 Linear functions
4 Exercise 4
5 Exercise 5 Linear functions
6 Exercise 6
7 Exercise 7
8 Exercise 8
9 Exercise 9 linear functions

A series of third grade math exercises on linear functions is always a positive for the student who wants to progress in math.

You will find in these math exercises on linear functions, the following concepts:

calculation of an image;
antecedent calculation;
calculation of the directing coefficient;
Plot the curve of a linear function;
calculation of percentages (increase and decrease).

Linear functions are a type of mathematical function that are used to model linear relationships between variables. In the third grade, students study linear functions and their use in various contexts in detail.

A linear function is a function that can be written as f(x) = ax.

Complete the following table giving the images of the numbers -1.5 , – $\frac{1}{2}$ , 0 , 1, $\frac{3}{4}$ , and 2 by each of the proposed linear applications.

Indicate for each of the tables, if it is a proportionality table and, if it is the case, express the associated linear application, translating the correspondence between the first and the second line.

Table 1				Table 3
5	10	15	20	1,5	2	2,5	3
10	15	20	25	4,5	6	7,5	9
Table 2				Table 4
30	33	36	39	7	14	21	35
10	11	12	13	1	2	3	4

In each case, we know a number and its image by a linear application. Determine its coefficient and express it in the simplest form possible.

8 $\mapsto$ – 64	9 $\mapsto$ 6	7 $\mapsto$ 4.9	11 $\mapsto$ -32
0.3 $\mapsto$ 12	1.2 $\mapsto$ 0.4	– 2.5 $\mapsto$ – 8	25 $\mapsto$ – 5

Complete tables of values of linear applications using the properties of linearity.

Application 1					Application 2
3	36	18	4	-2	2	4	-4	10
		63				5			-15

Give the linear applications associated with the following situations using percentages:

Increase by 25%.
Decrease by 20%.
Decrease by 4%.
Increase by 10%.
Decrease by 75%.

Translate each of these linear applications by a percentage change:

x $\mapsto$ 1.35x	x $\mapsto$ 0.98x	x $\mapsto$ 3/2 x	x $\mapsto$ ¾ x	x $\mapsto$ 1.01 x
x $\mapsto$ 0.86x	x $\mapsto$ 1.31x	x $\mapsto$ 4/9 x	x $\mapsto$ 5/8 x	x $\mapsto$ 1.002x

Are the following points whose coordinates are given located on the line graphically representing the linear application x $\mapsto$ – 0.75x ?

A (-1 ; 0.75) B (-2 ; $\frac{3}{2}$ ) C (-0.2 ; – 0.15) D (- $\frac{4}{3}$ ; 1)

In the same frame of reference, represent graphically the linear applications defined by :

x $\mapsto$ x ; x $\mapsto$ – x ; x $\mapsto$ – 3x ; x $\mapsto$ – $\frac{3}{2}$ x

Associate each of the lines shown with one of the proposed linear applications.

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– $\frac{1}{2}$

$\frac{3}{4}$

x $\mapsto$ 3x

X $\mapsto$ -2x

X $\mapsto$ $\frac{,1}{4}$ x

X $\mapsto$ – $\frac{3}{4}$ x

X $\mapsto$ 0.3x