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**6. Tentukan nilai c yang mana garis 3x + cy = 5**
(Determine the value of \( c \) for which the line \( 3x + cy = 5 \))

a) **melalui titik (3,1)**  
   (passes through the point \( (3, 1) \))

b) **sejajar dengan sumbu-y**  
   (parallel to the y-axis)

c) **sejajar dengan garis \( 2x + y = -1 \)**  
   (parallel to the line \( 2x + y = -1 \))

d) **tegak lurus dengan garis \( y - 2 = 3(x + 3) \)**  
   (perpendicular to the line \( y - 2 = 3(x + 3) \))

Let's solve each part to determine the value of \( c \) for each condition:

---

### Part a: \( 3x + cy = 5 \) passes through \( (3, 1) \)

Substitute \( x = 3 \) and \( y = 1 \) into the equation:

\[
3(3) + c(1) = 5 \quad \Rightarrow \quad 9 + c = 5 \quad \Rightarrow \quad c = 5 - 9 = -4
\]

So, \( c = -4 \) for part (a).

---

### Part b: Parallel to the y-axis

For a line to be parallel to the y-axis, its equation must be in the form \( x = \text{constant} \), meaning there is no \( y \)-term. In the given equation \( 3x + cy = 5 \), the coefficient of \( y \) must be 0. Thus:

\[
c = 0
\]

So, \( c = 0 \) for part (b).

---

### Part c: Parallel to the line \( 2x + y = -1 \)

First, rewrite the equation \( 2x + y = -1 \) in slope-intercept form:

\[
y = -2x - 1
\]

The slope of this line is \( -2 \). For two lines to be parallel, they must have the same slope. The given line \( 3x + cy = 5 \) can be rewritten as:

\[
cy = -3x + 5 \quad \Rightarrow \quad y = \frac{-3}{c}x + \frac{5}{c}
\]

Thus, for the lines to be parallel, the slopes must be equal:

\[
\frac{-3}{c} = -2 \quad \Rightarrow \quad c = \frac{3}{2}
\]

So, \( c = \frac{3}{2} \) for part (c).

---

### Part d: Perpendicular to the line \( y - 2 = 3(x + 3) \)

Rewrite the line in slope-intercept form. Start with:

\[
y - 2 = 3(x + 3) \quad \Rightarrow \quad y - 2 = 3x + 9 \quad \Rightarrow \quad y = 3x + 11
\]

The slope of this line is \( 3 \). For two lines to be perpendicular, the product of their slopes must be \( -1 \). The slope of the given line \( 3x + cy = 5 \) is \( \frac{-3}{c} \), so:

\[
3 \times \frac{-3}{c} = -1 \quad \Rightarrow \quad \frac{-9}{c} = -1 \quad \Rightarrow \quad c = 9
\]

So, \( c = 9 \) for part (d).

---

### Summary of Values:

- \( c = -4 \) for part (a)
- \( c = 0 \) for part (b)
- \( c = \frac{3}{2} \) for part (c)
- \( c = 9 \) for part (d)

Would you like further details or clarification on any part?

Here are some related questions to deepen understanding:
1. What does it mean for two lines to be parallel in terms of their slopes?
2. How do you find the equation of a line given a point and a slope?
3. How do you check if two lines are perpendicular?
4. Can the value of \( c \) affect the direction or position of a line? Why?
5. How would you find the distance between two parallel lines?

**Tip:** When solving geometric problems involving lines, always rewrite equations in slope-intercept form to easily identify the slope and the y-intercept.

Tentukan nilai c yang mana garis 3x + cy = 5

Find the value of c in the equation 3x + cy = 5 with conditions such as passing through a point, parallelism to the y-axis, and perpendicularity to another line. Suitable for Grades 10-12.

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