Find the equation of a line passing through the point (2,8), and parallel to the line y=(5/6)x-1

To find the equation of a line passing through the point (2,8) and parallel to the line \( y = \frac{5}{6}x - 1 \), follow these steps:

1. **Identify the slope**: 
   The slope of the given line \( y = \frac{5}{6}x - 1 \) is \(\frac{5}{6}\) because it is in the form \( y = mx + b \) where \( m \) is the slope.

2. **Use the point-slope form**:
   Since the new line is parallel to the given line, it has the same slope, \(\frac{5}{6}\). The point-slope form of the equation of a line is:
   \[
   y - y_1 = m(x - x_1)
   \]
   Here, \( (x_1, y_1) = (2, 8) \) and \( m = \frac{5}{6} \).

3. **Substitute the point and slope into the point-slope form**:
   \[
   y - 8 = \frac{5}{6}(x - 2)
   \]

4. **Simplify the equation**:
   Distribute \(\frac{5}{6}\) on the right side:
   \[
   y - 8 = \frac{5}{6}x - \frac{5}{3}
   \]
   To isolate \( y \), add 8 to both sides:
   \[
   y = \frac{5}{6}x - \frac{5}{3} + 8
   \]
   Convert 8 to a fraction with a common denominator of 3:
   \[
   y = \frac{5}{6}x - \frac{5}{3} + \frac{24}{3}
   \]
   Combine the constants:
   \[
   y = \frac{5}{6}x + \frac{19}{3}
   \]

So, the equation of the line passing through the point (2, 8) and parallel to the line \( y = \frac{5}{6}x - 1 \) is:
\[
y = \frac{5}{6}x + \frac{19}{3}
\]

Would you like further details or have any questions about this solution?

Here are some related questions to expand your understanding:

1. How do you determine the slope of a line given its equation in standard form?
2. What changes in the equation if the new line is perpendicular instead of parallel?
3. How can you convert the equation \( y = \frac{5}{6}x + \frac{19}{3} \) into standard form \( Ax + By = C \)?
4. How do you find the equation of a line given two points on the line?
5. What is the significance of the y-intercept in the equation of a line?
6. How do you derive the slope-intercept form from the general form of a linear equation?
7. What are the steps to graph the line \( y = \frac{5}{6}x + \frac{19}{3} \) on a coordinate plane?
8. How do you verify if a given point lies on the line \( y = \frac{5}{6}x + \frac{19}{3} \)?

**Tip:** When working with fractions in linear equations, it can be helpful to convert them to a common denominator to simplify addition and subtraction of the constants.

Learn how to find the equation of a line parallel to y=(5/6)x-1 passing through the point (2,8). This problem involves using the concept of parallel lines and point-slope form in linear equations. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation