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Cari persamaan garis lurus yang selari dengan garis lurus yang diberi

To find the equation of a line parallel to the given line \(4y + x = 25\), we first need to determine the slope of the given line.

### Step 1: Rewrite the given line in slope-intercept form

The given line is:

\[
4y + x = 25
\]

To rewrite this in the slope-intercept form (\(y = mx + c\)), solve for \(y\):

\[
4y = -x + 25 \implies y = -\frac{1}{4}x + \frac{25}{4}
\]

Here, the slope (\(m\)) of the line is \(-\frac{1}{4}\).

### Step 2: Identify the slope of the parallel line

Since parallel lines have the same slope, the slope of the line we want to find is also \(-\frac{1}{4}\).

### Step 3: Use the point-slope form to find the equation of the parallel line

We are given a point \((5, 1)\) that lies on the parallel line. The point-slope form of a line is:

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

Substitute the slope \(m = -\frac{1}{4}\) and the point \((x_1, y_1) = (5, 1)\):

\[
y - 1 = -\frac{1}{4}(x - 5)
\]

### Step 4: Simplify to slope-intercept form

Expand and simplify:

\[
y - 1 = -\frac{1}{4}x + \frac{5}{4}
\]

Add 1 to both sides:

\[
y = -\frac{1}{4}x + \frac{5}{4} + 1
\]

Convert 1 to a fraction:

\[
y = -\frac{1}{4}x + \frac{5}{4} + \frac{4}{4}
\]

Combine like terms:

\[
y = -\frac{1}{4}x + \frac{9}{4}
\]

### Conclusion

The equation of the line that is parallel to \(4y + x = 25\) and passes through the point \((5, 1)\) is:

\[
\boxed{y = -\frac{1}{4}x + \frac{9}{4}}
\]

Would you like more details, or do you have any other questions?

### Related Questions:
1. What is the equation of a line perpendicular to \(4y + x = 25\) passing through a different point?
2. How do you find the distance between two parallel lines?
3. Can you explain how to find the y-intercept and x-intercept of a line?
4. How do you determine if two lines are parallel or perpendicular just from their equations?
5. How do you find the intersection point of two lines?

### Tip:
When identifying parallel lines, remember that they will always have the same slope.

Learn how to find the equation of a line parallel to 4y + x = 25 that passes through the point (5, 1). This problem involves linear equations, parallel lines, and the point-slope form. Suitable for Grades 9-12.

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