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

To find the equation of a line, we can use the **point-slope form** of the equation of a line:

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

Where:
- \((x_1, y_1)\) is a point on the line (in this case, \((8, 3)\))
- \(m\) is the slope of the line (in this case, \(-\frac{1}{4}\))

Substitute the values:

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

Now, simplify the equation:

1. Distribute the slope on the right-hand side:
   \[
   y - 3 = -\frac{1}{4}x + 2
   \]

2. Add 3 to both sides to solve for \(y\):
   \[
   y = -\frac{1}{4}x + 2 + 3
   \]
   \[
   y = -\frac{1}{4}x + 5
   \]

Thus, the equation of the line is:

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

Would you like more details or have any questions about this?

Here are 5 related questions to explore further:
1. How would the equation change if the slope was positive?
2. Can you find the equation of a line parallel to this one through a different point?
3. How do you find the x-intercept of this line?
4. What is the y-intercept of this line, and how does it relate to the equation?
5. How would you write the equation in standard form?

**Tip:** When solving for the equation of a line, always check if you need to simplify further to get the slope-intercept form: \(y = mx + b\).

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

Learn how to find the equation of a line that passes through the point (8,3) with a slope of -1/4. This step-by-step solution explains the use of point-slope and slope-intercept forms, making it easy for students in Grades 8-10 to understand key algebraic concepts.

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