Write the equation of the line that passes through (1, 2) and is parallel to 2x - 5y = 8

To find the equation of the line that passes through the point \((1, 2)\) and is parallel to the line \(2x - 5y = 8\), we follow these steps:

### Step 1: Find the slope of the given line.
The equation of the line is given in the standard form:
\[
2x - 5y = 8
\]
To find the slope, \(m\), we first rewrite the equation in slope-intercept form \(y = mx + b\), where \(m\) is the slope.

Starting with:
\[
2x - 5y = 8
\]

Subtract \(2x\) from both sides:
\[
-5y = -2x + 8
\]

Divide every term by \(-5\):
\[
y = \frac{2}{5}x - \frac{8}{5}
\]

So, the slope \(m\) of the given line is:
\[
m = \frac{2}{5}
\]

### Step 2: Use the slope-point form to write the equation of the parallel line.
Since parallel lines have the same slope, the line passing through \((1, 2)\) will also have a slope of \(\frac{2}{5}\).

The point-slope form of a line is given by:
\[
y - y_1 = m(x - x_1)
\]
Substitute \(m = \frac{2}{5}\), \(x_1 = 1\), and \(y_1 = 2\):
\[
y - 2 = \frac{2}{5}(x - 1)
\]

### Step 3: Simplify the equation.
Distribute the slope \(\frac{2}{5}\):
\[
y - 2 = \frac{2}{5}x - \frac{2}{5}
\]

Add 2 to both sides to solve for \(y\):
\[
y = \frac{2}{5}x - \frac{2}{5} + \frac{10}{5}
\]
\[
y = \frac{2}{5}x + \frac{8}{5}
\]

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

Would you like any 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 are the properties of parallel lines in the coordinate plane?
3. How can the point-slope form be converted to the standard form of a line equation?
4. What is the significance of the slope-intercept form in graphing lines?
5. How do you determine if two lines are parallel just by looking at their equations?

**Tip:** Always convert the given line equation to slope-intercept form to easily identify the slope, which is crucial for finding parallel and perpendicular lines.

Find the equation of the line passing through (1, 2) and parallel to 2x - 5y = 8 using the point-slope form and the concept of parallel lines. This problem explains how to determine the slope of a given line and apply it to write the equation of the parallel line. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation