What is the equation of the line that passes through the point (5,2) and has a
slope of -6

If the given slope is –6/5, the equation is

y –2 = –6/5(x -5)

The attachment shows the graph of this equation.

The point-slope form is y = –6x/5 + 8

Step-by-step explanation:  The basic form for a point-slope equation is

y - b = m(x - a)

a is the x-value from the given coordinate, b is the y-value form the given coordinate, m is the slope. x and y are the variables in the function.

The slope, m, is given: -6/5   Substitute for m

Given coordinate points (5,2) substitute the x-value in place of a and the y-value in place of b

Rewrite the equation:

y - b = m(x - a) becomes

y - 2 = –6/5(x - 5)

it would be 6xy and -16xy.