The problem asks to find the equation of a line with a given slope = 3 that passes through the point $(3, 5)$.

We will use the point-slope form of a line, which is:

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

Where:

• $m$ is the slope,
• $(x_1, y_1)$ is the point on the line.

Here:

• $m = 3$,
• $(x_1, y_1) = (3, 5)$.

Substituting these values into the point-slope form:

$y - 5 = 3(x - 3)$

Now, simplify the equation:

$y - 5 = 3x - 9$

Adding 5 to both sides:

$y = 3x - 4$

Thus, the equation of the line in slope-intercept form is:

$y = 3x - 4$

Do you need more details or have any further questions?

Here are 5 related questions to expand your understanding:

1. How do you derive the point-slope form of a line from its geometric properties?
2. What is the difference between point-slope and slope-intercept forms of a line?
3. Can you convert this equation into standard form $Ax + By = C$?
4. What happens to the line equation if the slope is negative?
5. How would the equation change if the line passed through a different point with the same slope?

Tip: The slope of a line measures its steepness and can be calculated as the change in $y$ divided by the change in $x$ between two points.