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Which is an equation of the line with a slope of 2 that passes through (3,1)?

We are tasked with finding the equation of a line that has a slope of 2 and passes through the point \((3,1)\). To determine this, we use the point-slope form of a line, which is given by:

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

where \( m \) is the slope, and \( (x_1, y_1) \) is a point on the line.

### Step 1: Plug in the given values
- Slope \( m = 2 \)
- Point \( (x_1, y_1) = (3, 1) \)

Substituting these values into the point-slope form:

\[
y - 1 = 2(x - 3)
\]

### Step 2: Compare with the given options
Looking at the options provided in the image, the first equation matches:

\[
y - 1 = 2(x - 3)
\]

Thus, the correct equation is the first one.

### Answer: 
The correct equation of the line is the first option: \( y - 1 = 2(x - 3) \).

Do you need further details or explanations? 

Here are 5 related questions:
1. How do you convert from point-slope form to slope-intercept form?
2. Can a line passing through \((3, 1)\) have a different slope and still pass through the same point?
3. How do you find the y-intercept from the point-slope form equation?
4. What is the general equation of a line in slope-intercept form?
5. Can you explain what parallel and perpendicular slopes are?

**Tip:** To quickly identify the correct equation, always check the slope and the point provided in the problem with the general point-slope form.

Find the equation of a line with a slope of 2 that passes through the point (3,1). This problem involves using the point-slope formula, y - y1 = m(x - x1), and is suitable for students in Grades 7-9.

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