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To find the point-slope form of a line passing through the points \((1, 4)\) and \((6, -11)\), we first need to determine the slope (\(m\)) of the line using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

where \((x_1, y_1) = (1, 4)\) and \((x_2, y_2) = (6, -11)\).

### Step 1: Calculate the slope

\[
m = \frac{-11 - 4}{6 - 1} = \frac{-15}{5} = -3
\]

So, the slope of the line is \(-3\).

### Step 2: Write the point-slope form

The point-slope form of a line is given by:

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

Using the first point \((1, 4)\) and the slope \(m = -3\), we get:

\[
y - 4 = -3(x - 1)
\]

Thus, the point-slope form of the line is:

\[
y - 4 = -3(x - 1)
\]

Would you like more details on how to graph this or any other questions?

### Related Questions:
1. How can you convert the point-slope form to slope-intercept form?
2. What is the significance of the slope in the context of a real-world problem?
3. How would the equation change if you used the point \((6, -11)\) as the starting point?
4. Can you find the midpoint between the two given points?
5. How can you verify if another point lies on the line represented by the equation?

**Tip:** In point-slope form, you can use any point on the line, but using different points will yield different-looking equations that still represent the same line.

Find the point-slope form of the line passing through the given points. Use the first point as (x1, y1). Passing through (1,4) and (6, -11).

Learn how to find the point-slope form of a line passing through the points (1, 4) and (6, -11). This solution involves calculating the slope and applying the point-slope formula, making it suitable for students in Grades 9-12.

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