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

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 $l$.

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!