Write the equation of the line that passes through the points left parenthesis, 9, comma, minus, 1, right parenthesis(9,−1) and left parenthesis, minus, 7, comma, 4, right parenthesis(−7,4). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

To find the equation of the line passing through the points \((9, -1)\) and \((-7, 4)\), we follow these steps:

### 1. Find the slope of the line (denoted by \(m\)):

The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Substituting the given points \((9, -1)\) and \((-7, 4)\):

\[
m = \frac{4 - (-1)}{-7 - 9} = \frac{4 + 1}{-7 - 9} = \frac{5}{-16} = -\frac{5}{16}
\]

### 2. Use the point-slope form of the equation of a line:

The point-slope form is given by:

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

Using the point \((9, -1)\) and the slope \(m = -\frac{5}{16}\):

\[
y - (-1) = -\frac{5}{16}(x - 9)
\]

Simplifying the equation:

\[
y + 1 = -\frac{5}{16}(x - 9)
\]

This is the equation of the line in point-slope form.

Would you like more details on solving it further, or have any questions?

Here are 5 related questions:
1. How do you convert from point-slope form to slope-intercept form?
2. What happens when the line is vertical or horizontal?
3. How can you check if a point lies on a line?
4. How do you find the distance between two points?
5. How do you find the equation of a line parallel to a given line?

**Tip**: The slope of a vertical line is undefined, while a horizontal line has a slope of zero.

Write the equation of the line that passes through the points (9,−1) and (−7,4). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Learn how to find the equation of a line passing through the points (9,−1) and (−7,4) using the point-slope form. This solution covers the slope formula and algebraic concepts relevant to students in Grades 8-10.

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