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What is the Ax + By = C (where A > 0, and A, B, and C are integers with no common factors) of the equation of the line that passes through (8,-3) with a slope of -5/6

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The line's equation, Ax + By = C, with A > 0, has a slope of -A/B. For a line passing through (8,-3) with slope -5/6, the equation is -5x/6 + B(y-3) = C.

The equation of a line in the form Ax + By = C, where A > 0, represents a line with a slope of -A/B. In this case, the line passes through the point (8,-3) and has a slope of -5/6. To find the equation, we can substitute the values of the point and slope into the equation. First, let's find the value of A:

Plug in the x-coordinate of the point (-3) for x in the equation Ax + By = C: A(8) + B(-3) = C.

Apply the given slope (-5/6) to find the value of A: -5/6 = A.

Plug in the values of A, B, and the x and y coordinates of the point into the equation to find C: -5/6(8) + B(-3) = C.

Combine like terms and solve for B and C.

The equation of the line is -5x/6 + B(y-3) = C.

User DrMarbuse
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