The general format for equation of a straight line is:
y = mx + c
Where m = gradient, c = y intercept = -6.
The point format is (x, y).
Note, the x intercept is the value of x, when y = 0. Therefore, x intercept of 6, means at that point y = 0. Therefore the point is (6,0).
Note, the y intercept is the value of y when x = 0. Therefore, y intercept of -6, means at that point x = 0. Therefore the point is (0,-6).
Gradient between (6, 0) and (0, -6).
Gradient, m = (y2 - y1) / (x2 - x1) = (-6 - 0)/(0 - 6) = -6/-6 = 1
Gradient m = 1.
y = mx + c = 1x + (-6) = x - 6
y = x - 6. That is the equation of the line