How to find the value of k

Question

How to find the value of k if point f has the coordinates of (-2,9) and point g has the coordinates of (8,k) and the slope is -4/5

Answer 1

First find the equation for the line using y = mx + b, where m = slope and b = y-intercept

y = mx + b

9 = -4/5 (-2) + b

9 = 8/5 + b

9 - 8/5 = b

9 - 1 3/5 = b

7 2/5 = b

Now that we have the equation, y = -4/5x + 7 2/5 we can use this to find the value of k in (8,k)

y = -4/5x + 7 2/5

k = -4/5(8) + 7 2/5

k = -32/5 + 7 2/5

k = -6 2/5 + 7 2/5

k = 1