Write an equation of the line containing the given point and parallel to the given line.  Express your answer in the form yequalsmxplusb.
​(negative 2​,2​); 8xequals9yplus5

To find the equation of the line containing the point \((-2, 2)\) and parallel to the given line \(8x = 9y + 5\), follow these steps:

### Step 1: Rewrite the given line in slope-intercept form (\(y = mx + b\))
Start by converting the given equation into slope-intercept form.

\[ 8x = 9y + 5 \]

First, solve for \(y\):

\[ 9y = 8x - 5 \]

\[ y = \frac{8}{9}x - \frac{5}{9} \]

So, the slope \(m\) of the given line is \(\frac{8}{9}\).

### Step 2: Use the slope-point form to find the equation of the new line
Since the lines are parallel, the new line will have the same slope \(m = \frac{8}{9}\). Use the point-slope form of a line equation:

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

Where:
- \(m = \frac{8}{9}\)
- \((x_1, y_1) = (-2, 2)\)

Substitute these values into the equation:

\[ y - 2 = \frac{8}{9}(x + 2) \]

### Step 3: Simplify to slope-intercept form (\(y = mx + b\))
Distribute the slope \(\frac{8}{9}\) on the right side:

\[ y - 2 = \frac{8}{9}x + \frac{8}{9} \times 2 \]

\[ y - 2 = \frac{8}{9}x + \frac{16}{9} \]

Now, add 2 (which is \(\frac{18}{9}\) in terms of ninths) to both sides to solve for \(y\):

\[ y = \frac{8}{9}x + \frac{16}{9} + \frac{18}{9} \]

\[ y = \frac{8}{9}x + \frac{34}{9} \]

### Final Answer:
The equation of the line in the form \(y = mx + b\) is:

\[
y = \frac{8}{9}x + \frac{34}{9}
\]

Would you like further details or have any questions?

Here are some related questions:

1. How do you find the equation of a line perpendicular to a given line?
2. What is the significance of the slope in parallel lines?
3. How do you convert a line equation from standard form to slope-intercept form?
4. Can you find the equation of a line passing through two points?
5. How do you interpret the y-intercept in a linear equation?

**Tip:** Always check if two lines are parallel by comparing their slopes. Parallel lines have the same slope.

Learn how to write the equation of a line parallel to 8x = 9y + 5, passing through the point (-2, 2). This problem involves using the point-slope form and slope-intercept form of a line equation. Suitable for high school students.

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