We know the line runs through -2,3 and 2,5.
it also runs through 2, 5 and 6,k.
since all points are on the line, they're colinear, and therefore the line runs also through -2,3 and 6,k.
keeping in mind that line maintains a constant slope, therefore, the slope for -2,3 and 2,5, has to be the same slope as for 2,5 and 6,k.
what is the slope of -2,3 and 2,5 anyway?
![\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~{{ -2}} &,&{{ 3}}~) % (c,d) &&(~{{ 2}} &,&{{ 5}}~) \end{array} \\\\\\ % slope = m slope = {{ m}}\implies \cfrac{\stackrel{rise}{{{ y_2}}-{{ y_1}}}}{\stackrel{run}{{{ x_2}}-{{ x_1}}}}\implies \cfrac{5-3}{2-(-2)}\implies \cfrac{5-3}{2+2}\implies \cfrac{2}{4}\implies \cfrac{1}{2}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Bccccccccc%7D%0A%26%26x_1%26%26y_1%26%26x_2%26%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0A%26%26%28~%7B%7B%20-2%7D%7D%20%26%2C%26%7B%7B%203%7D%7D~%29%20%0A%25%20%20%28c%2Cd%29%0A%26%26%28~%7B%7B%202%7D%7D%20%26%2C%26%7B%7B%205%7D%7D~%29%0A%5Cend%7Barray%7D%0A%5C%5C%5C%5C%5C%5C%0A%25%20slope%20%20%3D%20m%0Aslope%20%3D%20%7B%7B%20m%7D%7D%5Cimplies%20%0A%5Ccfrac%7B%5Cstackrel%7Brise%7D%7B%7B%7B%20y_2%7D%7D-%7B%7B%20y_1%7D%7D%7D%7D%7B%5Cstackrel%7Brun%7D%7B%7B%7B%20x_2%7D%7D-%7B%7B%20x_1%7D%7D%7D%7D%5Cimplies%20%5Ccfrac%7B5-3%7D%7B2-%28-2%29%7D%5Cimplies%20%5Ccfrac%7B5-3%7D%7B2%2B2%7D%5Cimplies%20%5Ccfrac%7B2%7D%7B4%7D%5Cimplies%20%5Ccfrac%7B1%7D%7B2%7D)
and since we know the slope of 2,5 and 6,k is the same, then,