## All Tasks

#### Race (Intermediate-Modelling )

Three friends decided to take a run. Ana used a bicycle, Filipa and Joana used cars. Joana's car is faster than Filipa's.
Each function of the figure corresponds to the race of each of the friends.
The expression $g(5)=125$ means that:

# Linear functions

Modeling

9

#### Devaluation of a product (E_M)

Due to wear, the value (V) of a product decrease with time (t). We can then consider the devaluation of a product as a linear function. Knowing that the value of a machine today is 1000 euros, and estimating that in 5 years it will be 250 euros, what will its total devaluation be after 6 years?

# Linear functions

Modeling

9

#### Positive and negative slopes

Can you identify which slopes are positive and which are negative?
Select all and only those graphs that have positive slopes.

# Linear functions

Training

8

#### From table to law

If x and y of the table are proportional, find the law of a proportional function that fits to the data given in the table.

# Unassigned

Training

8

#### Intersection of linear functions

a) Calculate the point of intersection of the following two lines. Round to two decimal places for the input.
function 1: $y_1 = -1,5x + 3$
function 2: $y_2 = 3x + 6$
b) Calculate how the parameter $m$ of the line $y_3$ must be chosen so that the two lines $y_3$ and $y_4$ intersect at the position $x_0=3$. Round to two decimal places for the input.
function 1: $y_3 = m⋅x+3$
function 2: $y_4 = -2,5x + 10$

# Linear functions

Training

8

#### Gradient triangle

Consider the given linear function. The slope m indicates how much the function value changes when moving one unit in x-direction.
To determine this change, we need to identify any two points on the graph. Therefore, we use the gradient triangle. This is explained in the hints.
After you have read all hints carefully, you will be asked to apply what you have learned: to calculate the slope of the graph given in the task picture. Calculate its slope and enter your solution in the checkboxes.

# Linear functions

Learning

8