Final answer:
The equation of the line that passes through the points (8, -1) and (2, -5) can be found by calculating the slope, using the point-slope form of the equation, and converting it to standard form. After calculation, the equation in standard form is -2x + 3y = -19. However, this does not match any of the provided answer choices.
Step-by-step explanation:
To find the equation of the line that passes through the points (8, -1) and (2, -5), we first need to calculate the slope (m) of the line, which is the rise divided by the run between two points. We use the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given points into the formula yields:
m = (-5 - (-1)) / (2 - 8)
m = (-4) / (-6) = 2/3
Now, using the point-slope form of a line, which is y - y1 = m(x - x1), and choosing the point (8, -1), we have:
y + 1 = (2/3)(x - 8)
To convert this into standard form (Ax + By = C), we multiply through by 3 to eliminate the fraction:
3(y + 1) = 2(x - 8)
3y + 3 = 2x - 16
Subtracting 2x and 3 from both sides to get the x and y terms on one side:
-2x + 3y = -16 - 3
-2x + 3y = -19, which is the equation of the line in standard form.
Note that none of the answer choices (a. y = 2x - 17, b. y = -2x + 17, c. y = 2x + 17, d. y = -2x - 17) provided in point-slope form match the correct equation calculated. There might be a mistake in the available choices or in the question as presented.