To do this problem, it is important to rewrite the equation into slope-intercept form, or y = mx + b. Once you have solved for y, the coefficient in front of the x is the slope and b is the intercept. Therefore,
6x - 7y = 42
6x = 42 + 7y
6x - 42 = 7y
(6x-42)/7 = y
y = (6/7)x -(42/7)
y = (6/7)x - 6
the slope, m, equals 6/7, while the intercept, b, equals -6.