Final answer:
To find the equation of a line with a slope of -5/6 that passes through (8,-3) in the form Ax + By = C, we start with the point-slope form, plug in our values, simplify, and rearrange into standard form resulting in the equation 5x + 6y = 22.
Step-by-step explanation:
The student is asking for the equation of a line in the form Ax + By = C that passes through the point (8,-3) with a slope of -5/6, where A, B, and C are integers with no common factors and A is positive. To find the equation of this line, we need to use the point-slope form, which is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. First, we plug in the point (8, -3) and the slope -5/6 to get the equation in point-slope form:
y - (-3) = (-5/6)(x - 8)
Next, we simplify and rearrange to get the standard form Ax + By = C: y + 3 = (-5/6)x + (40/6)
Multiply every term by 6 to clear the fractions: 6y + 18 = -5x + 40
Then, we can rewrite the equation to have positive A, and in the form Ax + By = C: 5x + 6y = 22
Finally, we verify no common factors exist between A, B, and C. The equation 5x + 6y = 22 is the answer and fits the required format.