Answer:
(d) 2
Explanation:
You want the sum (a+b) of the solution (a, b) to the system of equations represented by the table of values ...
- f(1) = 3, f(4) = 9
- g(1) = 5, g(4) = 20
Graph
The attached graph shows the point of intersection is ...
(a, b) = (1/3, 5/3)
Then a+b = 1/3 +5/3 = 6/3 = 2, matching choice D.
Equations
The slope of the line representing function f(x) is ...
m = (y2 -y1)/(x2 -x1)
m = (9 -3)/(4 -1) = 6/3 = 2
The intercept is ...
b = y -mx
b = 3 -2(1) = 1
So, the equation for f(x) is ...
f(x) = 2x +1
The slope of the line representing g(x) is ...
m = (20 -5)/(4 -1) = 15/3 = 5
And the intercept is ...
b = 5 -5(1) = 0
giving the equation ...
g(x) = 5x
Point
The point of intersection is found where the functions have the same value:
f(a) = g(a) = b
2a +1 = 5a
1 = 3a
a = 1/3
b = 5a = 5/3
a+b = 1/3 +5/3 = 2 . . . . . choice D
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