Write an equation of the line containing the given point and parallel to the given line.  Express your answer in the form 

yequals=mxplus+b.

​(negative 2−2​,22​); 

88xequals=99yplus+5

To find the equation of the line that passes through the point \((-2, 2)\) and is parallel to the 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 \(8x = 9y + 5\) into slope-intercept form:

\[
8x = 9y + 5
\]

Subtract 5 from both sides to isolate the \(9y\) term:

\[
8x - 5 = 9y
\]

Now, divide both sides by 9 to solve for \(y\):

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

This gives us the slope \(m = \frac{8}{9}\).

### Step 2: Use the point-slope form to find the equation of the new line
Since the new line is parallel to the given line, it will have the same slope \(m = \frac{8}{9}\). We can use the point-slope form of the line equation, which is:

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

Where \((x_1, y_1) = (-2, 2)\). Substitute the values:

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

### 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 to both sides to solve for \(y\) (remember that 2 is equivalent to \(\frac{18}{9}\) in terms of ninths):

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

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

### 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 more details or have any questions?

Here are some related questions:

1. How do you find the slope of a line given two points?
2. How can you determine if two lines are perpendicular?
3. What is the point-slope form of a linear equation?
4. How do you convert a linear equation from slope-intercept form to standard form?
5. What is the significance of the y-intercept in a linear equation?

**Tip:** When given a problem involving parallel lines, remember that they always share the same slope.

Learn how to find the equation of a line parallel to 8x = 9y + 5 passing through the point (-2, 2). This problem involves using the slope of parallel lines and the point-slope form of a line equation. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation