Final answer:
To find the equation of a line with a slope of 3 passing through (6, -5) in Standard Form, we use the point-slope formula and convert it to Standard Form to get 3x - y = 23, which is not listed in the options provided.
Step-by-step explanation:
The student is looking for the equation of a line in Standard Form that has a slope of 3 and passes through the point (6, -5). To find the equation of the line in Standard Form (Ax + By = C), we can first use the point-slope form of the line, which is given by:
y - y1 = m(x - x1)
Where (x1, y1) is the point the line passes through, and m is the slope of the line. Substituting the given point and slope:
y - (-5) = 3(x - 6)
y + 5 = 3x - 18
To convert this to Standard Form, we need to rearrange the equation so that 'x' and 'y' are both on the left side:
-3x + y = -18 - 5
-3x + y = -23
This equation is now in Standard Form. However, none of the options provided match this result. There may be an error in the options or a misunderstanding in the question as posed. Typically, the coefficients in Standard Form are integers, and the 'A' term is non-negative. Thus, we would multiply through by -1 to get:
3x - y = 23
But again, this is not listed in the provided options.