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The segment AB is a line joining the points A( -1 , -3) and B(3, 7).
The equation of the line joining them can be taken to be the function f(x).
The equation of the line is given by:
y + 3 = [( -3 - 7)/(-1 - 3)](x + 1)
=> y + 3 = (-10/-4)(x + 1)
=> y +3 = (5/2)(x + 1)
=> y = (5/2)(x + 1) - 3
=> y = (5x + 5 - 6)/2
=> y = (5x - 1)/2
Therefore f(x) = (5x - 1)/2
We'll write the form of the linear function:
f(x) = ax + b
y = mx + n, where m represents the slope of the line and n represents the y intercept.
In this case, the function f(x) has as graph the line AB.
According to the rule, a point belongs to a line if the coordinates of the point verify the equation of the line.
A is on the line y = ax+b if and only if yA = a*xA + b
We'll substitute the coordinates xA and yA and we'll get:
-3 = a*(-1) + b
-3 = -a + b (1)
B belongs to the line y = ax+b if and only if yB = a*xB + b.
We'll substitute the coordinates xB and yB and we'll get:
7 = a*3 + b (2)
We'll subtract (2) from (1):
3a + b + a - b = 7 + 3
We'll combine and eliminate like terms:
4a = 10
a = 5/2
b - a = -3
b = a - 3
b = 5/2 - 3
b = -1/2
The function f(x) whose graph is represented by the line AB:
f(x) = (5/2)*x - 1/2
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