write an equation in slope intercept form for the line that satisfies each set of conditions. passes through (-6, -6) and is parallel to y= 4/3x + 2

To find the equation of a line that is **parallel** to the given line \( y = \frac{4}{3}x + 2 \) and passes through the point \( (-6, -6) \), follow these steps:

1. **Identify the slope of the given line**: The equation of the given line is in slope-intercept form, \( y = mx + b \), where \( m \) represents the slope. Here, \( m = \frac{4}{3} \).

   Since parallel lines have the same slope, the slope of the new line is also \( \frac{4}{3} \).

2. **Use the point-slope form of the equation**: The point-slope form is
   \[
   y - y_1 = m(x - x_1)
   \]
   where \( (x_1, y_1) \) is the point the line passes through and \( m \) is the slope. Plugging in \( m = \frac{4}{3} \) and the point \( (-6, -6) \):

   \[
   y - (-6) = \frac{4}{3}(x - (-6))
   \]
   Simplifying:
   \[
   y + 6 = \frac{4}{3}(x + 6)
   \]

3. **Simplify the equation**:
   Now distribute the \( \frac{4}{3} \):
   \[
   y + 6 = \frac{4}{3}x + \frac{4}{3} \times 6
   \]
   \[
   y + 6 = \frac{4}{3}x + 8
   \]

4. **Solve for \( y \)** to put it in slope-intercept form:
   \[
   y = \frac{4}{3}x + 8 - 6
   \]
   \[
   y = \frac{4}{3}x + 2
   \]

Thus, the equation of the line is:
\[
y = \frac{4}{3}x + 2
\]

Even though it passes through the point \( (-6, -6) \), the slope and intercept match the original line's equation because they are parallel.

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Would you like further clarification? Here are five related questions for practice:

1. What is the equation of a line perpendicular to \( y = \frac{4}{3}x + 2 \) that passes through \( (-6, -6) \)?
2. If the slope of a line is \( -\frac{4}{3} \), what is the equation of the line passing through \( (2, 3) \)?
3. How do you find the slope of a line given two points?
4. How does the slope-intercept form of a line change if the slope is negative?
5. What does it mean geometrically when two lines are parallel?

**Tip**: When lines are parallel, they always share the same slope but differ in their intercepts.

Learn how to write the equation of a line that passes through (-6, -6) and is parallel to y = 4/3x + 2. This problem covers key algebra concepts such as slope-intercept form, point-slope form, and the properties of parallel lines. Suitable for students in Grades 8-10.

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