Equation of a Line



If three points \(A=(k,k+2),\) \(B=(0,k-6)\) and \(C=(k-4,k)\) all lie on the same line, what is the value of \(k?\)

The \( x \)- and \( y \)-intercepts of a line have the same value. If the line passes through \(P=(7,-6)\) and \(Q=(-6,k),\) what is the value of \(k?\)

Consider the two points \((-1, -1)\) and \((3, 7).\) If a circle passes through these two points, then which of the following cannot also be a point on the circle?

What is the sum of all the values of \(k\) that make three points \(A=(1,k),\) \(B=(k,1)\) and \(C=(10,10)\) lie on the same line?

Consider the line passing through two points \(P=(1, 10)\) and \(Q=(-1, 3) \). If the line also passes through point \(R=(17, a)\), what is the value of \(a\)?


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