f the graphs of the equations 5x - 2y = 5 and6x+ky 9 are perpendicular, what is the valueof k?

The first step is to convert both equations into slope-intercept form (y = mx + b), where m is the slope of the line.

The first equation is 5x - 2y = 5. To convert this into slope-intercept form, we isolate y:

-2y = -5x + 5 y = (5/2)x - 5/2

So, the slope (m1) of the first line is 5/2.

The second equation is 6x + ky = 9. Again, we isolate y:

ky = -6x + 9 y = (-6/k)x + 9/k

So, the slope (m2) of the second line is -6/k.

If two lines are perpendicular, the product of their slopes is -1. So, we set m1 * m2 = -1 and solve for k:

(5/2) * (-6/k) = -1 -15/k = -1 k = 15

So, the value of k is 15.