To find the equation of the line passing through the points $(2, 1)$ and $(0, -5)$, follow these steps:

Step 1: Find the slope ($m$) of the line

The formula for the slope is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute $(x_1, y_1) = (2, 1)$ and $(x_2, y_2) = (0, -5)$: $m = \frac{-5 - 1}{0 - 2} = \frac{-6}{-2} = 3$

Step 2: Use the point-slope form of the equation

The point-slope form of a line is: $y - y_1 = m(x - x_1)$ Using the slope $m = 3$ and one of the points, say $(2, 1)$: $y - 1 = 3(x - 2)$

Step 3: Simplify to slope-intercept form ($y = mx + b$)

Expand and simplify: $y - 1 = 3x - 6$ $y = 3x - 5$

Final Equation

The equation of the line is: $y = 3x - 5$

Would you like a step-by-step explanation or further details?

Here are 5 questions to expand your understanding:

1. How do you determine the slope of a line given two points?
2. What is the difference between point-slope and slope-intercept form?
3. Can you find the equation of a line parallel to this one passing through a different point?
4. How would the equation change if the points were swapped?
5. How do you graph this equation on a coordinate plane?

Tip: Always simplify fractions when calculating the slope for a cleaner equation.