To find the equation of a line in slope-intercept form (which is $y = mx + b$), we are given:

• The slope $m = 3$
• A point $(2, -5)$ through which the line passes.

Step 1: Use the point-slope form equation

The point-slope form of a line is:

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

Substitute $m = 3$, $x_1 = 2$, and $y_1 = -5$:

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

Simplify:

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

Step 2: Expand and solve for $y$

Now, distribute the slope $3$ on the right side:

$y + 5 = 3x - 6$

Subtract $5$ from both sides to solve for $y$:

$y = 3x - 6 - 5$

$y = 3x - 11$

Final Answer:

The equation of the line in slope-intercept form is:

$y = 3x - 11$

Would you like more details on any step or have questions about the process?

---

Here are five related questions you might find helpful:

1. How do you calculate the slope when given two points?
2. What is the significance of the y-intercept in a line equation?
3. How do you convert from point-slope form to slope-intercept form?
4. Can you derive the equation of a horizontal line through a given point?
5. How does the slope value affect the steepness of the line?

Tip: When solving for the y-intercept $b$, plugging a point into the slope-intercept equation $y = mx + b$ can be a quick method!