To find the equation of a line given the slope and a point through which it passes, we use the point-slope form of a line's equation:

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

Where:

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

Given:

• Slope $m = 2$,
• Point $(x_1, y_1) = (3, 5)$.

Substituting these values into the point-slope formula:

$y - 5 = 2(x - 3)$

Now, let's simplify this equation:

$y - 5 = 2x - 6$

Add 5 to both sides:

$y = 2x - 1$

Thus, the equation of the line is:

$y = 2x - 1$

Would you like further details or clarification?

Here are 5 related questions for further exploration:

1. How can we rewrite the equation of a line in standard form?
2. What is the y-intercept of the line from this equation?
3. How would the equation change if the slope were negative?
4. Can you find the equation of a line parallel to this one but passing through a different point?
5. How can you verify if a point lies on this line?

Tip: The point-slope form is particularly useful when you know a point and the slope of the line.