What is an equation of the line that passes through the point left parenthesis, 6, comma, 6, right parenthesis(6,6) and is parallel to the line 2, x, minus, y, equals, 52x−y=5?

To find the equation of a line that passes through the point \((6, 6)\) and is parallel to the line \(2x - y = 5\), follow these steps:

### Step 1: Identify the slope of the given line
The equation of the given line is \(2x - y = 5\). First, rewrite this equation in slope-intercept form \(y = mx + b\), where \(m\) is the slope:

\[
2x - y = 5 \quad \Rightarrow \quad -y = -2x + 5 \quad \Rightarrow \quad y = 2x - 5
\]

So, the slope \(m\) of the given line is \(2\).

### Step 2: Use the point-slope form for the new line
Since the new line is parallel to the given line, it will have the same slope, \(m = 2\). The point-slope form of a line is:

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

where \((x_1, y_1)\) is the point through which the line passes, and \(m\) is the slope. Here, the point is \((6, 6)\) and \(m = 2\), so:

\[
y - 6 = 2(x - 6)
\]

### Step 3: Simplify the equation
Expand and simplify the equation:

\[
y - 6 = 2x - 12
\]
\[
y = 2x - 12 + 6
\]
\[
y = 2x - 6
\]

### Final Answer:
The equation of the line that passes through the point \((6, 6)\) and is parallel to the line \(2x - y = 5\) is:

\[
y = 2x - 6
\]

Would you like further clarification or more details?

Here are 5 related questions to explore:
1. How do you find the equation of a line perpendicular to another line?
2. What is the general form of a linear equation?
3. How do you calculate the distance between a point and a line?
4. What are the properties of parallel and perpendicular lines?
5. How can you determine if two lines are parallel from their equations?

**Tip:** When converting a linear equation to slope-intercept form, always solve for \(y\) to identify the slope clearly!

What is an equation of the line that passes through the point (6, 6) and is parallel to the line 2x − y = 5?

Learn how to find the equation of a line that passes through the point (6, 6) and is parallel to the line 2x − y = 5. This problem involves the concept of parallel lines, linear equations, and the point-slope form. Suitable for students in Grades 8-10.

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