Final answer:
To find the equation of a line with a given slope and passing through a given point, use the point-slope form of a line equation. Substituting the values and simplifying the equation will give you the final equation in the form Ax + By = C.
Step-by-step explanation:
To find the equation of a line with a given slope and passing through a given point, we can use the point-slope form of a line equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the given slope.
Substituting the values m = 7/4 and (x1, y1) = (6, -2) into the equation, we get y - (-2) = (7/4)(x - 6).
We can simplify this equation by multiplying both sides by 4 to get 4y + 8 = 7(x - 6), which simplifies to 4y + 8 = 7x - 42. Rearranging this equation gives us the final equation in the form Ax + By = C as 7x - 4y = 50.