For what values of h does the equation have real solutions. √(3x-h)= x+3

Square both side to get

3x-h = (x+3)^2

distribute the squared

3x - h = x^2 + 6x + 9

subtract 3x from both sides

-h = x^2 + 3x + 9

The answer will only have real solutions if the right side is factorable

h= -19, and 2.25 are both values that would make the right side factorable

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c