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Answer:
a. y = -1/3x +7/3
b. f(6) = 1/3
Step-by-step explanation:
The two given points are (1, 2) and (4, 1). The slope of the line between them is given by the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (1 -2)/(4 -1) = -1/3
The point-slope form of the equation of the line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
We can add k to both sides of this equation and substitute for our slope (-1/3) and the first point (1, 2). This gives ...
y = m(x -h) +k
y = -1/3(x -1) +2
y = -1/3x +7/3 . . . . eliminate parentheses
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b. The value of y when x=6 is ...
y = -1/3(6) +7/3 = (-6 +7)/3
y = 1/3
That is, for f(x) = -1/3x +7/3, ...
f(6) = 1/3
