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.