## All Tasks

#### 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

#### value (Beginner-Exercising)

Consider the function f defined by $f(x) = -5x -1$.
Find the value of $x$ whose image is $−8$.
(Present the result with one decimal place)

# Linear functions

Training

9

#### Intersection

Given two linear functions $y_1 = \frac{x}{2} + 2$ and $y_2=-x+5$. Can you find their point of intersection?

# Linear functions

Training

8