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The problem asks for the equation of a line in two different forms: point-slope form and slope-intercept form. The given information is:

- Slope \( m = -\frac{2}{9} \)
- A point on the line: \( (1, -7) \)

### 1. **Point-Slope Form:**
The point-slope form of a line is given by the formula:

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

Where:
- \( (x_1, y_1) \) is the given point (1, -7)
- \( m \) is the slope \( -\frac{2}{9} \)

Substitute the values into the formula:

\[
y - (-7) = -\frac{2}{9}(x - 1)
\]

Simplify:

\[
y + 7 = -\frac{2}{9}(x - 1)
\]

This is the equation in **point-slope form**.

### 2. **Slope-Intercept Form:**
The slope-intercept form is given by:

\[
y = mx + b
\]

We already know the slope \( m = -\frac{2}{9} \), and we need to solve for \( b \), the y-intercept. Use the given point \( (1, -7) \) to substitute \( x = 1 \) and \( y = -7 \) into the slope-intercept form equation:

\[
-7 = -\frac{2}{9}(1) + b
\]

Simplify:

\[
-7 = -\frac{2}{9} + b
\]

Now solve for \( b \):

\[
b = -7 + \frac{2}{9}
\]

Convert \(-7\) into a fraction with denominator 9:

\[
b = -\frac{63}{9} + \frac{2}{9} = -\frac{61}{9}
\]

So, the slope-intercept form is:

\[
y = -\frac{2}{9}x - \frac{61}{9}
\]

Would you like further details or clarification on any step?

### Related Questions:
1. How can I verify if a point lies on the line using an equation?
2. What is the general form of a linear equation?
3. How do you convert point-slope form to standard form?
4. Can you explain how to interpret the slope in real-world contexts?
5. How would the equation change if the point was different but the slope remained the same?

### Tip:
When dealing with fractions in equations, always try to keep terms in a common denominator to simplify operations like addition or subtraction.

Use the given conditions to write an equation for the line in point-slope form and slope-intercept form. Slope = -2/9, passing through (1, -7).

Learn how to write the equation of a line with slope -2/9 passing through the point (1, -7) in both point-slope and slope-intercept forms. This step-by-step solution explains core concepts like point-slope form and slope-intercept form. Ideal for students in Grades 8-10.

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