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Problem

We can parameterize the ray from C through P as a function of t:
space, R, left parenthesis, t, right parenthesis, equals, left parenthesis, 1, minus, t, right parenthesis, C, plus, t, P
With C at left parenthesis, 0, comma, 0, right parenthesis and P at left parenthesis, 4, comma, minus, 2, right parenthesis, R, left parenthesis, t, right parenthesis intersects a line defined by the equation:
y, equals, x, minus, 9
If the intersection point is I and I, equals, R, left parenthesis, t, start superscript, times, end superscript, right parenthesis, what is the value of t, start superscript, times, end superscript?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i