Find the equation of the line which is parallel to the given line and also passes through the given point. Show your steps and working out. Y= 2x - 4 (2,5)

To find the equation of the line that is parallel to \( y = 2x - 4 \) and passes through the point \( (2,5) \), we follow these steps:

### Step 1: Identify the slope of the given line
The equation of the given line is:
\[
y = 2x - 4
\]
This is in slope-intercept form, \( y = mx + b \), where \( m \) is the slope of the line. Here, the slope \( m \) is \( 2 \).

Since parallel lines have the same slope, the line we are looking for will also have a slope of \( 2 \).

### Step 2: Use the point-slope form
To find the equation of a line when we know its slope and a point it passes through, we can use the point-slope form of a line:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is a point on the line, and \( m \) is the slope.

Here:
- The slope \( m = 2 \),
- The point \( (x_1, y_1) = (2,5) \).

Substitute these values into the point-slope form:
\[
y - 5 = 2(x - 2)
\]

### Step 3: Simplify the equation
Now, distribute the \( 2 \) on the right-hand side:
\[
y - 5 = 2x - 4
\]
Next, add \( 5 \) to both sides to solve for \( y \):
\[
y = 2x + 1
\]

### Final Answer
The equation of the line that is parallel to \( y = 2x - 4 \) and passes through the point \( (2,5) \) is:
\[
y = 2x + 1
\]

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Would you like any further details or have any questions?

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**Related Questions:**

1. How would you find the equation of a line perpendicular to \( y = 2x - 4 \) that passes through \( (2,5) \)?
2. What is the slope of a line parallel to \( y = -3x + 7 \)?
3. If a line passes through \( (3, -2) \) and has a slope of \( -1 \), what is its equation?
4. How can you verify if two lines are parallel?
5. What is the slope-intercept form of a line passing through \( (0,4) \) and \( (2,8) \)?

**Tip:** In point-slope form, use any point on the line along with the slope to derive the line equation.

Find the equation of a line that is parallel to y = 2x - 4 and passes through the point (2,5). This solution explains step-by-step how to identify slopes of parallel lines, apply the point-slope form, and simplify the result. Ideal for Grades 8-10.

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