Final answer:
The equation of the line passing through the points (6, -11) and (7, 2) in standard form is neither a), b), c), nor d) based on the calculated slope and standard form procedure. The correct equation should be 13x - y = 89, which is not listed among the provided options.
Step-by-step explanation:
To find the equation of the line in standard form that passes through the points (6, -11) and (7, 2), we'll first calculate the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in our points:
m = (2 - (-11)) / (7 - 6) = 13
With the slope known, pick one of the points, (6, -11), to write the point-slope form of the equation:
y - (-11) = 13(x - 6)
Expanding this:
y 11 = 13x - 78
Now, rearrange to standard form, Ax + By = C:
13x - y = 78 + 11
13x - y = 89
Depending on how we define 'standard form', we might consider multiplying the equation by -1 if the format requires A to be negative:
-13x + y = -89
None of the options provided by the student match our results. It's possible there is a mistake in either the calculation or the provided options. Ensure calculations are correct and ask the student to double-check the options given.