The question asks for the equation of the line that passes through the points $(0, -6)$ and $(1, 0)$. Let's solve it step by step.

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

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

Step 2: Use the point-slope form of a line

The point-slope form of a line is: $y - y_1 = m(x - x_1)$ Substitute $m = 6$ and one of the points, say $(0, -6)$, into the formula: $y - (-6) = 6(x - 0)$ Simplify: $y + 6 = 6x$

Step 3: Write the equation in slope-intercept form

Simplify further to get: $y = 6x - 6$

Final Answer:

The equation of the line is: $y = 6x - 6$

Would you like a detailed explanation for any of the steps?

Here are 5 related questions to expand your understanding:

1. How do you find the slope of a vertical line?
2. What is the equation of a line that passes through two points with the same $y$-coordinate?
3. How can you convert an equation in point-slope form to standard form?
4. What is the geometric interpretation of the slope of a line?
5. How would the equation change if one of the points were shifted?

Tip:

When solving for the equation of a line, double-check your slope calculation—it determines the steepness of the line!