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We are asked to find the equation of a line that passes through the point \( (8, 3) \) and has a slope of \( -\frac{1}{4} \).

The general form of the equation of a line is:

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

where \( m \) is the slope, and \( (x_1, y_1) \) is a point on the line.

In this case:
- \( m = -\frac{1}{4} \)
- \( (x_1, y_1) = (8, 3) \)

Substituting these values into the equation:

\[
y - 3 = -\frac{1}{4}(x - 8)
\]

Now, simplify:

\[
y - 3 = -\frac{1}{4}x + 2
\]

Add 3 to both sides:

\[
y = -\frac{1}{4}x + 2 + 3
\]

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

Thus, the equation of the line is:

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

Would you like further clarification, or do you have any other questions?

Here are some related questions you might find helpful:
1. How do you convert an equation from point-slope form to slope-intercept form?
2. What is the significance of the slope in a linear equation?
3. How would the equation change if the slope were positive \( \frac{1}{4} \) instead of negative?
4. How do you find the x-intercept and y-intercept from the equation \( y = -\frac{1}{4}x + 5 \)?
5. Can the equation of a line be expressed in standard form using integer coefficients?

**Tip:** Always double-check your slope and points when writing the equation of a line, as small sign errors can lead to different results!

What is the equation of the line that passes through the point (8, 3) and has a slope of -1/4?

Find the equation of the line passing through the point (8, 3) with a slope of -1/4. This problem explores point-slope and slope-intercept forms, essential concepts in algebra for students in grades 8-10.

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