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The question asks you to write the equation of a line passing through the point (-1, 6) and parallel to the line \( x + 3y = 5 \). We are to find the equation in both **slope-intercept form** and **standard form**.

### Step-by-step solution:

1. **Find the slope of the given line:**
   The given line is \( x + 3y = 5 \). Let's rewrite it in slope-intercept form \( y = mx + b \), where \( m \) is the slope.

   \[
   3y = -x + 5
   \]
   \[
   y = -\frac{1}{3}x + \frac{5}{3}
   \]

   So, the slope of the given line is \( m = -\frac{1}{3} \).

2. **Use the slope-point form to find the equation of the new line:**
   The line we are looking for is **parallel** to \( x + 3y = 5 \), so it will have the **same slope**, \( m = -\frac{1}{3} \), and it passes through the point (-1, 6).

   The point-slope form of the equation of a line is:
   \[
   y - y_1 = m(x - x_1)
   \]
   Substituting \( m = -\frac{1}{3} \), \( x_1 = -1 \), and \( y_1 = 6 \):
   \[
   y - 6 = -\frac{1}{3}(x + 1)
   \]
   \[
   y - 6 = -\frac{1}{3}x - \frac{1}{3}
   \]
   \[
   y = -\frac{1}{3}x + \frac{17}{3}
   \]

   So, the equation in **slope-intercept form** is:
   \[
   y = -\frac{1}{3}x + \frac{17}{3}
   \]

3. **Convert the equation to standard form:**
   To convert \( y = -\frac{1}{3}x + \frac{17}{3} \) to standard form \( Ax + By = C \), multiply through by 3 to eliminate the fractions:
   \[
   3y = -x + 17
   \]
   Rearranging:
   \[
   x + 3y = 17
   \]

   So, the equation in **standard form** is:
   \[
   x + 3y = 17
   \]

### Final answers:
- (a) The equation of the line in **slope-intercept form** is \( y = -\frac{1}{3}x + \frac{17}{3} \).
- (b) The equation of the line in **standard form** is \( x + 3y = 17 \).

Would you like further explanation or have any other questions?

### Related questions:
1. How do you find the slope of a line from its equation in standard form?
2. What are the characteristics of parallel lines in terms of their slopes?
3. How do you convert an equation from point-slope form to slope-intercept form?
4. Why is it important to express equations in different forms (slope-intercept, standard, etc.)?
5. How do you find the equation of a line that is perpendicular to a given line?

**Tip:** To convert any linear equation to standard form, ensure that the coefficients are integers, and the coefficient of \( x \) is positive.

Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-1, 6) and parallel to x + 3y = 5.

Learn how to write the equation of a line passing through (-1, 6) and parallel to x + 3y = 5 in both slope-intercept and standard form. This problem covers key concepts like slope, point-slope form, and the conversion to standard form.

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