Write the equation of a line that goes through the point (2,3) and is parallel to the line y = 3x+4.

To find the equation of a line that passes through the point \( (2,3) \) and is parallel to the line \( y = 3x + 4 \), follow these steps:

### Step 1: Identify the slope of the given line  
The equation \( y = 3x + 4 \) is in slope-intercept form \( y = mx + b \), where \( m \) is the slope.  
Thus, the slope of the given line is:
\[
m = 3
\]

### Step 2: Use the slope for the new line  
Since parallel lines have the **same slope**, the slope of the desired line is also:
\[
m = 3
\]

### Step 3: Apply the point-slope form of a line  
The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope. Substituting \( (x_1, y_1) = (2, 3) \) and \( m = 3 \):

\[
y - 3 = 3(x - 2)
\]

### Step 4: Simplify the equation  
Distribute the slope:
\[
y - 3 = 3x - 6
\]
Add 3 to both sides:
\[
y = 3x - 3
\]

### Final Answer  
The equation of the line parallel to \( y = 3x + 4 \) and passing through the point \( (2,3) \) is:
\[
y = 3x - 3
\]

Would you like to see more details or have any questions?

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Here are 5 related questions:
1. What is the general formula for finding the slope between two points?
2. How do you determine if two lines are perpendicular?
3. Can you write the equation of a line perpendicular to \( y = 3x + 4 \) passing through \( (2,3) \)?
4. How do you convert a linear equation into point-slope form from slope-intercept form?
5. What happens if two lines have the same slope and intercept?

**Tip:** Parallel lines always have equal slopes, but different intercepts (unless they are the same line).

Find the equation of a line parallel to y = 3x + 4 that passes through the point (2,3). This problem covers key algebra concepts, including slope-intercept form, point-slope form, and the parallel line theorem. Suitable for students in Grades 8-10.

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