The slope can be found by using the formula: m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))m=y2−y1x2−x1
Where mm is the slope and (color(blue)(x_1, y_1)x1,y1) and (color(red)(x_2, y_2)x2,y2) are the two points on the line.
Substitute the values given in the problem and solve for KK:
1 = (color(red)(4) - color(blue)(-K))/(color(red)(-1) - color(blue)(2))1=4−−K−1−2
1 = (4 + color(blue)(K))/(-3)1=4+K−3
color(red)(-3) xx 1 = color(red)(-3) xx (4 + color(blue)(K))/(-3)−3×1=−3×4+K−3
-3 = cancel(color(red)(-3)) xx (4 + color(blue)(K))/(color(red)(cancel(color(black)(-3))))
-3 = 4 + color(blue)(K)
-3 - color(red)(4) = 4 + color(blue)(K) - color(red)(4)
-3 - color(red)(4) = 4 - color(red)(4) + color(blue)(K)
-7 = 0 + color(blue)(K)
-7 = color(blue)(K)
color(blue)(K) = -7
