To find the equation of the line passing through the point $(2,1)$ with a slope $m=3$, we can use the point-slope form of a line's equation:

$y - y_1 = m(x - x_1)$

Where:

• $(x_1, y_1)$ is the point the line passes through, which is $(2,1)$,
• $m$ is the slope, which is 3.

Substituting these values into the point-slope formula:

$y - 1 = 3(x - 2)$

Now, simplify this equation:

$y - 1 = 3x - 6$

$y = 3x - 6 + 1$

$y = 3x - 5$

So, the equation of the line is:

$y = 3x - 5$

Would you like more details on this process or have any questions?

Here are 5 related questions for further exploration:

1. What is the y-intercept of the line with equation $y = 3x - 5$?
2. How would the equation change if the slope was negative?
3. Can you find the equation of a line parallel to this one passing through a different point?
4. How do you find the slope of a line given two points on the line?
5. What is the equation of a line perpendicular to the one you found?

Tip: The point-slope form is particularly useful when you know one point and the slope of the line, but don’t have the y-intercept.