Use point-slope form to write the equation of a line that passes through the point left parenthesis, 18, comma, minus, 17, right parenthesis(18,−17) with slope minus, one quarter− 
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The point-slope form of a line's equation is given by the formula:

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

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

You are given:
- The point \((x_1, y_1) = (18, -17)\)
- The slope \(m = -\frac{1}{4}\)

Substitute these values into the point-slope form:

\[
y - (-17) = -\frac{1}{4}(x - 18)
\]

Simplify the equation:

\[
y + 17 = -\frac{1}{4}(x - 18)
\]

If you want to leave it in point-slope form, you're done. However, if you prefer to rewrite it in slope-intercept form (i.e., \(y = mx + b\)), we can expand and simplify further:

Distribute the slope on the right-hand side:

\[
y + 17 = -\frac{1}{4}x + \frac{18}{4}
\]

Simplify \(\frac{18}{4}\):

\[
y + 17 = -\frac{1}{4}x + \frac{9}{2}
\]

Subtract 17 from both sides to solve for \(y\):

\[
y = -\frac{1}{4}x + \frac{9}{2} - 17
\]

Convert 17 to a fraction with the same denominator:

\[
y = -\frac{1}{4}x + \frac{9}{2} - \frac{34}{2}
\]

Combine the constants:

\[
y = -\frac{1}{4}x - \frac{25}{2}
\]

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

\[
y = -\frac{1}{4}x - \frac{25}{2}
\]

Would you like more details on any step? 

Here are some related questions:
1. How would you graph a line using the point-slope form?
2. What is the significance of the slope in this equation?
3. How do you convert point-slope form to standard form?
4. How does the slope affect the direction of the line?
5. How can you verify if a point lies on this line?

**Tip:** Understanding point-slope form makes it easier to write equations of lines when given a point and slope.

Use point-slope form to write the equation of a line that passes through the point (18,−17) with slope −1/4.

Learn how to use the point-slope form to write the equation of a line passing through the point (18,−17) with a slope of −1/4. The solution includes steps to simplify the equation and convert it to slope-intercept form. Suitable for students in Grades 8-10.

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