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The problem asks for the equation of a line in slope-intercept form that passes through the point \((-7, 4)\) and is parallel to the line given by the equation:

\[
y = -\frac{2}{7}x + 6
\]

### Step 1: Identify the slope of the given line

The slope-intercept form of a line is:

\[
y = mx + b
\]

where \(m\) is the slope. From the given equation \(y = -\frac{2}{7}x + 6\), the slope \(m\) is \(-\frac{2}{7}\).

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

Since the line we are looking for is parallel to the given line, it must have the same slope. Therefore, the slope of the new line is also \(-\frac{2}{7}\).

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

We can use the point-slope form to find the equation of the line:

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

where \((x_1, y_1)\) is the point the line passes through, and \(m\) is the slope. Substituting \(x_1 = -7\), \(y_1 = 4\), and \(m = -\frac{2}{7}\):

\[
y - 4 = -\frac{2}{7}(x + 7)
\]

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

Now, expand and solve for \(y\):

\[
y - 4 = -\frac{2}{7}x - \frac{2}{7} \times 7
\]
\[
y - 4 = -\frac{2}{7}x - 2
\]
\[
y = -\frac{2}{7}x + 2
\]

Thus, the equation of the line in slope-intercept form is:

\[
y = -\frac{2}{7}x + 2
\]

Would you like more details on this solution or have any further questions?

### Related Questions:
1. How do you find the slope of a line given two points?
2. What is the difference between parallel and perpendicular lines?
3. How do you convert a point-slope equation to slope-intercept form?
4. What does it mean when two lines have the same slope?
5. How can you find the y-intercept of a line given a point and slope?

### Tip:
For parallel lines, always remember that they share the same slope, but their y-intercepts are different unless they are the same line.

What is the equation in slope-intercept form of the line that passes through (-7, 4) and is parallel to y = -2/7x + 6?

Find the equation of a line passing through the point (-7, 4) and parallel to y = -2/7x + 6. Learn key algebraic concepts like the slope-intercept form and point-slope form. Suitable for students in Grades 8-10.

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