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

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:

1. calculation of an image;
2. antecedent calculation;
3. calculation of the directing coefficient;
4. Plot the curve of a linear function;
5. 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.

## Exercise 1

Complete the following table giving the images of the numbers -1.5 , – , 0 , 1, , and 2 by each of the proposed linear applications.

 -1,5 – $\frac{1}{2}$ 0 1 $\frac{3}{4}$ 2 x $\mapsto$ 3x X $\mapsto$ -2x X $\mapsto$ $\frac{,1}{4}$x X $\mapsto$ – $\frac{3}{4}$ x X $\mapsto$ 0.3x

## Exercise 2

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

## Exercise 3 Linear functions

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

## Exercise 4

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

## Exercise 5 Linear functions

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

1. Increase by 25%.
2. Decrease by 20%.
3. Decrease by 4%.
4. Increase by 10%.
5. Decrease by 75%.

## Exercise 6

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

## Exercise 7

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

A (-1 ; 0.75) B (-2 ; ) C (-0.2 ; – 0.15) D (- ; 1)

## Exercise 8

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

x x ; x – x ; x – 3x ; x x

## Exercise 9 linear functions

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

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