Find the equation for the line that passes through the points  
(
2
,
7
)
  and  
(
−
9
,
−
7
)
 . Give your answer in point-slope form. You do not need to simplify

To find the equation of the line in point-slope form, we follow these steps:

### Step 1: Find the slope (\(m\))
The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

For the points \( (2, 7) \) and \( (-9, -7) \), we substitute into the formula:

\[
m = \frac{-7 - 7}{-9 - 2} = \frac{-14}{-11} = \frac{14}{11}
\]

### Step 2: Use point-slope form
The point-slope form of a line's equation is:

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

You can choose either point \((x_1, y_1)\). I'll use the point \( (2, 7) \). Substituting the values into the formula:

\[
y - 7 = \frac{14}{11}(x - 2)
\]

So, the equation of the line in point-slope form is:

\[
y - 7 = \frac{14}{11}(x - 2)
\]

Would you like more details or clarifications?

---

Here are five related questions for further practice:

1. How do you convert the equation to slope-intercept form?
2. What is the equation of the line passing through \((3, -2)\) and \((6, 4)\)?
3. What is the slope of a vertical line?
4. How do you find the midpoint between two points?
5. Can you determine the distance between two points?

**Tip:** Always remember, in point-slope form, you can use either point to write the equation of the line.

Find the equation for the line that passes through the points (2, 7) and (-9, -7). Give your answer in point-slope form. You do not need to simplify.

Learn how to find the equation of a line in point-slope form that passes through the points (2, 7) and (-9, -7). This detailed step-by-step guide covers the slope formula and point-slope form, making it suitable for students in Grades 8-10.

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