You put the equation in slope-intercept form by solving for y.
.. 7y = -6x -42 . . . . . .subtract 6x
.. y = (-6/7)x -6 . . . . . divide by 7
Compare this to the pattern
.. y = mx +b
The slope is the coefficient of x, m = -6/7.
The intercept is the constant term, b = -6.
