Find the equation of a line passing through the point (-1,1 ) and is parallel to 
the line 3X+4Y-7=0

To find the equation of the line passing through the point \((-1, 1)\) and parallel to the given line \(3x + 4y - 7 = 0\), we follow these steps:

### Step 1: Identify the slope of the given line
First, rewrite the given equation \(3x + 4y - 7 = 0\) in slope-intercept form \(y = mx + b\).

\[
3x + 4y - 7 = 0
\]
\[
4y = -3x + 7
\]
\[
y = -\frac{3}{4}x + \frac{7}{4}
\]

So, the slope \(m\) of the given line is \(-\frac{3}{4}\).

### Step 2: Use the slope for the parallel line
Since the lines are parallel, the slope of the line we are looking for is also \(-\frac{3}{4}\).

### Step 3: Use the point-slope form of a line
Now, we use the point-slope form of the equation of a line, which is:

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

Here:
- \((x_1, y_1) = (-1, 1)\) is the point the line passes through.
- \(m = -\frac{3}{4}\) is the slope.

Substituting these values:

\[
y - 1 = -\frac{3}{4}(x - (-1))
\]
\[
y - 1 = -\frac{3}{4}(x + 1)
\]

### Step 4: Simplify the equation
Expand the right-hand side:

\[
y - 1 = -\frac{3}{4}x - \frac{3}{4}
\]
Add 1 to both sides:

\[
y = -\frac{3}{4}x - \frac{3}{4} + 1
\]
\[
y = -\frac{3}{4}x + \frac{1}{4}
\]

### Final Answer:
The equation of the line is:

\[
y = -\frac{3}{4}x + \frac{1}{4}
\]

Let me know if you need further details!

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**Related Questions:**
1. How do you find the slope of a line from its equation?
2. What is the general form of a line equation in slope-intercept form?
3. How do you find the equation of a line perpendicular to a given line?
4. What is the point-slope form of a line equation?
5. How do parallel lines relate in terms of their slopes?

**Tip:** Remember, parallel lines always have equal slopes, but their intercepts can differ.

Find the equation of a line passing through the point (-1,1) and is parallel to the line 3X+4Y-7=0.

Learn how to find the equation of a line passing through the point (-1,1) and parallel to 3x + 4y - 7 = 0 using slope-intercept and point-slope forms. A step-by-step guide for high school students in Grades 9-11, covering key algebraic concepts.

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