Tentukan fungsi linier yang memenuhi Y=f(X) dan gambarkan garis fungsinya dari: -20-2Y = 30X

Untuk menentukan fungsi linier dari persamaan yang diberikan, kita mulai dengan mengubah bentuknya menjadi bentuk standar fungsi linier \( Y = f(X) \).

Persamaan awalnya adalah:

\[
-20 - 2Y = 30X
\]

### Langkah-langkah:

1. Pindahkan konstanta ke sisi kanan:
   \[
   -2Y = 30X + 20
   \]

2. Bagi kedua sisi dengan -2 untuk mendapatkan \( Y \):
   \[
   Y = \frac{30X + 20}{-2}
   \]

3. Sederhanakan persamaan:
   \[
   Y = -15X - 10
   \]

### Fungsi linier:
Jadi, fungsi linier yang memenuhi persamaan tersebut adalah:

\[
Y = -15X - 10
\]

### Grafis fungsi linier:
Fungsi \( Y = -15X - 10 \) memiliki gradien -15 dan titik potong sumbu-Y di \( -10 \). Sekarang, saya akan menggambarkan grafik dari fungsi ini.

It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can still plot the linear function manually or using any graphing tool based on the equation \( Y = -15X - 10 \).

Would you like more information or a breakdown of how to graph it by hand? Here are some questions to expand your understanding:

1. How do you determine the slope of a line from its equation?
2. How would you find the x-intercept of the function \( Y = -15X - 10 \)?
3. What effect does changing the slope have on the graph of a linear function?
4. How does the y-intercept affect the position of the line?
5. How can you use two points to draw a straight line graph?

**Tip:** To graph a line manually, calculate the y-values for two x-values (e.g., \(X = 0\) and \(X = 1\)) and plot these points on a coordinate plane. Then, draw a straight line through them.

Learn how to determine the linear function from the equation -20 - 2Y = 30X and graph the line. This step-by-step solution covers key algebraic concepts such as manipulating linear equations and understanding the slope-intercept form of a line. Suitable for students in Grades 8-10.

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