## All Tasks

#### 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

#### Route (Beginner-Modelling)

Joana goes from home to school for a part of the route on foot, another part by bicycle and a third part by bus. If the graph represents the route from home to school, how did she make the route?

# Functions & characteristics

Modeling

9

#### Graph (Intermediate-Learning)

The figure shows the graphs of 4 functions, match each function with its graph.

# Linear functions

Learning

9