Question

Find the value of k so that the line through the given points has slope m.

Answer 1

$(2k,3) \\ x_1=2k \\ y_1=3 \\ \\ (1,k) \\ x_2=1 \\ y_2=k \\ \\ \hbox{the slope: } m=\frac{y_2-y_1}{x_2-x_1}=\frac{k-3}{1-2k}$

The slope is equal to 2.
$\frac{k-3}{1-2k}=2 \\ k-3=2(1-2k) \\ k-3=2-4k \\ k+4k=2+3 \\ 5k=5 \\ k=\frac{5}{5} \\ \boxed{k=1}$