Line r has an equation of y–9=3(x–10). Line s includes the point (
–
2,
–
7) and is parallel to line r. What is the equation of line s?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

To find the equation of line \( s \), we need to follow these steps:

1. **Determine the slope of line \( s \)**:
   Since line \( s \) is parallel to line \( r \), they share the same slope. We first need to find the slope of line \( r \).

   The equation of line \( r \) is given as:
   \[
   y - 9 = 3(x - 10)
   \]
   This is in point-slope form, where the slope \( m = 3 \).

   Therefore, the slope of line \( s \) is also \( 3 \).

2. **Use the point-slope form to write the equation of line \( s \)**:
   Line \( s \) passes through the point \( (-2, -7) \) and has a slope of 3. We use the point-slope form of a line equation:
   \[
   y - y_1 = m(x - x_1)
   \]
   Substituting the point \( (-2, -7) \) for \( (x_1, y_1) \) and the slope \( m = 3 \), we get:
   \[
   y - (-7) = 3(x - (-2))
   \]
   Simplifying this equation:
   \[
   y + 7 = 3(x + 2)
   \]
   Distribute the 3 on the right-hand side:
   \[
   y + 7 = 3x + 6
   \]
   Subtract 7 from both sides:
   \[
   y = 3x + 6 - 7
   \]
   Simplifying further:
   \[
   y = 3x - 1
   \]

Thus, the equation of line \( s \) in slope-intercept form is:
\[
y = 3x - 1
\]

Would you like further details or have any questions?

Here are 5 related questions you might find useful:
1. How do you find the equation of a line perpendicular to a given line?
2. What is the difference between point-slope form and slope-intercept form?
3. How do you convert from standard form to slope-intercept form?
4. Can two lines be parallel if they have different slopes?
5. How do you find the slope of a line from its graph?

**Tip**: When two lines are parallel, their slopes are always equal.

Line r has an equation of y–9=3(x–10). Line s includes the point (-2, -7) and is parallel to line r. What is the equation of line s? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

This solution explains how to find the equation of a line parallel to another line, passing through the point (-2, -7). The problem involves using point-slope and slope-intercept forms and applying the concept of parallel lines with equal slopes. Suitable for students in Grades 8-10.

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