A direct variation function contains the points (-9, -3) and (-12,4). Which equation represents the function?
1 answer:
Answer:
Step-by-step explanation:
We can model this function using the equation of a line:
Where a is the slope of the line and b is the y-intercept.
To find the values of a and b, we can use the two points given:
(-9, -3):
(-12, 4):
If we subtract the second equation from the first one, we have:
Then, finding the value of b, we have:
So the equation is:
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It depends on how b approaches 0
If b is positive and gets closer to zero, then we say b is approaching 0 from the right, or from the positive side. Let's say a = 1. The equation a/b turns into 1/b. Looking at a table of values, 1/b will steadily increase without bound as positive b values get closer to 0.
On the other side, if b is negative and gets closer to zero, then 1/b will be negative and those negative values will decrease without bound. So 1/b approaches negative infinity if we approach 0 on the left (or negative) side.
The graph of y = 1/x shows this. See the diagram below. Note the vertical asymptote at x = 0. The portion to the right of it has the curve go upward to positive infinity as x approaches 0. The curve to the left goes down to negative infinity as x approaches 0.
