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The image shows a mathematical problem in Dutch. Here is the translation and interpretation of the text:

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**b.** The line \( l \) passes through the point \( B(9, 3) \) and is parallel to the line \( m: y = -\frac{1}{2}x + 4 \).

**Question:** Write the equation of line \( l \).

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### Solution:

Since line \( l \) is parallel to line \( m \), they have the same slope. The equation of line \( m \) is given as:

\[
y = -\frac{1}{2}x + 4
\]

Thus, the slope of line \( m \) is \( -\frac{1}{2} \). Since parallel lines have equal slopes, the slope of line \( l \) is also \( -\frac{1}{2} \).

Now, using the point-slope form of the line equation, which is:

\[
y - y_1 = m(x - x_1)
\]

where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope. For line \( l \), we have:
- \( (x_1, y_1) = (9, 3) \)
- \( m = -\frac{1}{2} \)

Substitute these values into the point-slope form:

\[
y - 3 = -\frac{1}{2}(x - 9)
\]

Simplifying:

\[
y - 3 = -\frac{1}{2}x + \frac{9}{2}
\]

Add 3 to both sides to isolate \( y \):

\[
y = -\frac{1}{2}x + \frac{9}{2} + 3
\]

Convert 3 into a fraction:

\[
y = -\frac{1}{2}x + \frac{9}{2} + \frac{6}{2}
\]

Now, simplify:

\[
y = -\frac{1}{2}x + \frac{15}{2}
\]

Thus, the equation of the line \( l \) is:

\[
y = -\frac{1}{2}x + \frac{15}{2}
\]

### Do you want more details or have any questions?

Here are some related questions:
1. How do you find the equation of a line given a point and the slope?
2. What is the significance of parallel lines having the same slope?
3. How can you convert a fraction into a decimal in a linear equation?
4. How does changing the point affect the equation of the line?
5. What if the lines were perpendicular instead of parallel? How would you find the equation?

**Tip:** Always remember that parallel lines share the same slope but differ in their y-intercepts!

De lijn l gaat door het punt B(9, 3) en is evenwijdig met de lijn m: y = -1/2x + 4. Stel de formule op van l.

Learn how to find the equation of a line passing through the point (9, 3) and parallel to the line y = -1/2x + 4. This problem covers linear equations, slope-intercept form, and the point-slope formula. Ideal for students in Grades 9-12.

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