find the line parallel to y=2x+4 thru (4,20)

To find the equation of a line parallel to \( y = 2x + 4 \) that passes through the point \( (4, 20) \), follow these steps:

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

### Step 2: Use the point-slope form of a line equation
The equation of a line with slope \( m \) that passes through a point \( (x_1, y_1) \) is given by the point-slope form:
\[
y - y_1 = m(x - x_1)
\]
Here, the slope \( m = 2 \), and the point is \( (4, 20) \).

### Step 3: Plug in the slope and point
Substitute \( m = 2 \), \( x_1 = 4 \), and \( y_1 = 20 \) into the point-slope formula:
\[
y - 20 = 2(x - 4)
\]

### Step 4: Simplify the equation
Expand and simplify the equation:
\[
y - 20 = 2x - 8
\]
\[
y = 2x - 8 + 20
\]
\[
y = 2x + 12
\]

So, the equation of the line parallel to \( y = 2x + 4 \) and passing through \( (4, 20) \) is:
\[
y = 2x + 12
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the slope of a perpendicular line?
2. How can you convert the point-slope form into slope-intercept form?
3. What is the significance of parallel and perpendicular slopes?
4. How do you find the distance between two parallel lines?
5. Can you find the equation of a line passing through two points?

**Tip:** When two lines are parallel, their slopes are always the same.

Learn how to find the equation of a line parallel to y = 2x + 4 that passes through the point (4, 20). This problem involves key linear algebra concepts such as parallel lines, point-slope form, and slope-intercept form. Suitable for students in Grades 8-10.

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