Question

Find the equation of the line with gradient 1/2 which passes through the point ( t², 2t). If this line passes through the point (-2, 1), find the possible values of t.​

Answer 1

We are given that the slope is $\frac{1}{2}$.

So the equation of the line has to be of the form $\frac{1}{2}x+c=y$.

We are given that one of the points is (-2,1). The point also has to follow the equation of the line as it lies on the line.

Thus,

          $\frac{1}{2}(-2)+c=1\\(-1)+c=1\\c=2$

The equation of the line is: $\frac{1}{2}x+2=y$

So for the point (t², 2t):

                                      $\frac{1}{2}t^2 +2=2t\\t^2+4=4t\\t^2+4-4t=0\\(t-2)^2=0$

The only possible value of t is 2.