Final answer:
After calculating the slope of the line passing through the points (-5, -4) and (1, -1) as 0.5, and using this to write the equation of the line, none of the multiple choice answers match the derived equation y = 0.5x - 1.5. Therefore, it appears there may be an error in the provided options.
Step-by-step explanation:
To find an equation for the line that passes through the points (-5, -4) and (1, -1), first we need to calculate the slope of the line using the following formula:
Slope (m) = (y2 - y1) / (x2 - x1)
Substituting the given points yields:
m = (-1 - (-4)) / (1 - (-5))
m = 3 / 6
m = 0.5
Now, we use the point-slope form of a line to write the equation. The point-slope form is y - y1 = m(x - x1). Let's use (-5, -4) as (x1, y1).
y - (-4) = 0.5(x - (-5))
y + 4 = 0.5(x + 5)
y + 4 = 0.5x + 2.5
y = 0.5x + 2.5 - 4
y = 0.5x - 1.5
Since none of the answer choices match exactly with our equation, we need to find an equivalent form by multiplying through by 2 to remove the fraction from the slope:
2y = x - 3
Divide through by 2 to isolate y:
y = x/2 - 3/2
y = 0.5x - 1.5
Again, this doesn't match any of the provided options, indicating a possible error in the choices.