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Let's work through the problems you shared in the image. The questions seem to be focused on finding equations for lines and determining linear functions.

### 1. Equation of the Line \( g \)

#### a) 
The line \( g \) has a slope of \( m = -4.5 \) and passes through point \( A(0| -3) \).

To find the equation, we can use the point-slope form:
\[
y - y_1 = m(x - x_1)
\]
Here, \( m = -4.5 \) and \( (x_1, y_1) = (0, -3) \).

So, the equation becomes:
\[
y + 3 = -4.5(x - 0) \implies y = -4.5x - 3
\]

#### b) 
The line \( g \) has a slope of \( m = 3 \) and passes through \( A(1|1.5) \).

Using the point-slope form again:
\[
y - 1.5 = 3(x - 1) \implies y - 1.5 = 3x - 3 \implies y = 3x - 1.5
\]

#### c) 
The line passes through \( A(-6|1) \) and is parallel to the line \( h \) with the equation \( y = -x + 2 \).

Since the lines are parallel, they have the same slope, \( m = -1 \). Using the point-slope form again:
\[
y - 1 = -1(x + 6) \implies y - 1 = -x - 6 \implies y = -x - 5
\]

#### d) 
The line passes through \( A(1| -2) \) and \( B(-2|10) \).

First, we calculate the slope \( m \) of the line:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{10 - (-2)}{-2 - 1} = \frac{12}{-3} = -4
\]

Now, using the point-slope form with point \( A(1| -2) \):
\[
y + 2 = -4(x - 1) \implies y + 2 = -4x + 4 \implies y = -4x + 2
\]

#### e) 
The line \( h \) is given by the equation \( y = 

Bestimmen Sie die Gleichung der Geraden g. Find the equation of line g with given slope, points, and parallel line conditions. Also, determine the linear function passing through given points.

Learn how to find the equation of a line using slopes and points, including cases where the line is parallel to another. Problems involve key concepts in linear equations, suitable for Grades 8-10.

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