Question

Find the value of k so that the line joining (3,k) and (-1, |k|) has the slope m=2

Answer 1

The two points given are as follows;

`\begin{gathered} (3,k)\text{ and} \\ (-1,|k|) \end{gathered}`

Where the slope is given as 2, we can determine the values of the y coordinates (that is k and |k|) as follows;

`\begin{gathered} \text{ Using the point-slope form;} \\ y_2-y_1=m(x_2-x_1) \\ y_2-y_1=2(-1-3) \\ y_2-y_1=-2-6 \\ y_2-y_1=-8 \\ \text{Given that the value of y}_2\text{ is an absolute value, we can derive that;} \\ |k|-k=-8 \\ \text{This cannot be solved except the answer on the right side is a positive} \\ In\text{ that case we would have;} \\ |k|-k=8 \\ |4|-\lbrack-4\rbrack=8 \\ |4|+4=8 \end{gathered}`

There is no solution to this question if the slope is positive 2.