The equation of lime k is y = - 1/5x-1/8 what is the equation of the line that us perpendicular to lime k and passes through (0,0)

Since the line will be perpendicular the slope will be the opposite reciprocal of - 1/5 which is 5. Using the ordered pair (0,0) we know the y intercept will be 0, so y = 5x is the equation

Line k: y=-1/5x-1/8 This is in y=mx+b form or slope-intercept form.

For a perpendicular line you switch the reciprocal of the slope. So, instead of - 1/5x for the slope, it would be 5. The (b) part represents the y intercept so you would change it to 0. Here is the new equation: y=5x-0.