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k = - 2

Step-by-step explanation:

Lines g(x) and f(x) passes through the points (2, 0), (0, 2) & (4, 0), (0, 4)

Since both the lines are parallel, so slopes of lines g(x) and f(x) would be same.

Therefore,

Slope of line g = Slope of line f = (2-0)/(0 - 2) = 2/-2 = - 1

Equation of line g(x)

For point (0, 2)

y- intercept (b) = 2

y = mx + b

g(x) = - 1x + 2 [y = g(x)]

g(x) = - x + 2

Equation of line f(x)

For point (0, 4)

y- intercept (b) = 4

y = mx + b

f(x) = - 1x + 4 [y = g(x)]

f(x) = - x + 4

It is given that:

g(x) = f(x) + k

g(x) - f(x) = k

(-x + 2) - (-x + 4) = k

-x + 2 + x - 4 = k

2 - 4 = k

-2 = k

k = - 2

step-by-step explan mxfcg'k; uafwgzfgjhklhgation:

step-by-step explanation: