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The question asks us to find the equation of a line with a slope of \(-4\) that passes through the point \((0, 2)\).

We can use the **point-slope form** of the equation of a line, which is given by:

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

Where:
- \(m\) is the slope of the line.
- \((x_1, y_1)\) is a point on the line.

### Step-by-step Solution:

1. The slope \(m = -4\), and the point \((x_1, y_1) = (0, 2)\).

2. Substituting these values into the point-slope form:

\[
y - 2 = -4(x - 0)
\]

3. Simplifying:

\[
y - 2 = -4x
\]

4. Solving for \(y\):

\[
y = -4x + 2
\]

Thus, the equation of the line is:

\[
\boxed{y = -4x + 2}
\]

Would you like more details or explanations on any step? Here are some related questions:

1. How do we determine the slope when given two points?
2. What are the different forms of a line's equation?
3. Can a line have an undefined slope? If yes, what does that mean?
4. How can we graph the equation \(y = -4x + 2\)?
5. What is the significance of the y-intercept in a linear equation?

**Tip:** The y-intercept is the value of \(y\) when \(x = 0\). It tells you where the line crosses the y-axis!

Find the equation of a line that has a slope of -4 and passes through the point (0, 2).

Learn how to find the equation of a line with a slope of -4 passing through the point (0, 2). This problem explores key concepts of algebra, including the point-slope form. Suitable for students in Grades 8-10.

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