SOLUTION: Find a real number k such that the line 3x-ky+2=0 has y-intercept -3 . Find the value of k.

Question 903961: Find a real number k such that the line 3x-ky+2=0 has y-intercept -3 . Find the value of k.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the y-intercept is the value of y when x is equal to 0.
this means that when x = 0, y = -3.
replace x with 0 and y with -3 in your original equation to get 3*0 - k*-3 + 2 = 0
simplify to get -k*-3 + 2 = 0
subtract 2 from both sides of the equation to get -k*-3 = -2
simplify to get 3*k = -2
divide both sides by 3 to get k = -2/3.
your solution should be good when k = -2/3.
to confirm, replace x with 0 and y with -3 and k with -2/3 in your original equation of 3x - ky + 2 = 0 to get 3*0 - (-2/3)*(-3) + 2 = 0.
simplify to get 0 - 2 + 2 = 0.
simplify further to get 0 = 0 which confirms the solution of k = -(2/3) is good.
a graph of your eqaution is shown below using k = (-2/3) to confirm that the solution is good from a graphical perspective.
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