The problem asks for the slope-intercept equation of the line that passes through the points (-1, -5) and (1, -1). Let's calculate step-by-step:

1. Find the slope (m):

The slope $m$ is calculated as: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting $(x_1, y_1) = (-1, -5)$ and $(x_2, y_2) = (1, -1)$: $m = \frac{-1 - (-5)}{1 - (-1)} = \frac{-1 + 5}{1 + 1} = \frac{4}{2} = 2$

2. Write the equation in slope-intercept form:

The slope-intercept form of a line is: $y = mx + b$ We now know $m = 2$, so the equation becomes: $y = 2x + b$

3. Find the y-intercept ($b$):

Substitute one of the given points, say $(-1, -5)$, into the equation $y = 2x + b$: $-5 = 2(-1) + b$ $-5 = -2 + b$ $b = -5 + 2 = -3$

4. Final equation:

The equation of the line is: $y = 2x - 3$

Correct answer:

The correct choice is: $\boxed{y = 2x - 3}$

Would you like a detailed explanation of any step?
Here are 5 related questions to expand your understanding:

1. How do you derive the slope formula for a straight line?
2. What is the importance of slope-intercept form in graphing?
3. How do you determine if two points lie on the same line?
4. Can you explain why substituting a point into the equation gives the y-intercept?
5. What is the geometric significance of the slope and y-intercept?

Tip: Always verify your equation by substituting both points to check if they satisfy the equation.