The student didn't make any mistake. The slope of the line between those points is 3/8.
Which is an equation in point-slope form for the line that passes through the points (−1,4) and (3,−4) ?
2 answers:
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Answer:
D . . . (best of the erroneous choices)
Step-by-step explanation:
Solving the first equation for x, we get ...
√(y -1) ≥ x
Solving the second equation for x, we get ...
x > 3
Substituting for x, we have ...
√(y -1) > 3
y -1 > 9
y > 10
Ordered pairs that are in the solution set will have coordinates ...
x > 3, y > 10
In interval notation that looks like ...
x ∈ (-∞, 3) and y ∈ (10, ∞)
The closest answer choice is the last one.
_____
You will note that x must be strictly greater than 3, so y cannot be equal to 10. The offered choice is in error on that point.
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You will also note that y is dependent on x. That is, one cannot pick a value of y greater than 10 independently of the value of x. In that sense, the solution is not "the set of all ordered pairs such that [x and y have independent limits]". Rather, it is the set of all ordered pairs such that √(y -1) ≥ x > 3.
