Answer: The value of k is -(1/3)
Explanation:
To find the equations, we can use the fact that:
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
Then we can find the equation for f(x) by knowing that it passes through the points:
(0,2) and (1, - 1)
Then its slope is:
a = (-1 - 2)/(1 - 0) = -3
f(x) = -3*x + b
And for the value of b, we can replace the values of one of the points in the equation, and solve it for b.
For example, if we remplace the values of the point (0,2), we have:
f(0) = 2 = -3*0 + b
2 = b
Then the equation is: f(x) = -3*x + b
We can do the same for g(x).
We can see that it passes through the points (0, 2) and (-2, 0)
Then the slope is:
a = (0 - 2)/(-2 - 0) = 1.
and as it also passes through the point (0, 2), we also will have:
g(0) = 2 = 1*0 + b
2 = b
Then the equation is: g(x) = x + 2
Now we have:
f(x) = -3*x + 2
g(x) = f(k*x) = -3*(k*x) + 2 = 1*x + 2
let's solve that for k.
-3*(k*x) + 2 = 1*x + 2
-3*k*x = x + 2 - 2
-3*k*x = x
-3*k = x/x
-3*k = 1
k = 1/-3 = -1/3
The value of k is -(1/3)