which data set represents an increasing linear function?
a) (1,-2),(3,1),(5,4),(7,7)
b) (1,1),(2,0),(3,-1),(4,-2)
c) (1,-3),(3,5),(5,11),(7,18)
d) (1,17),(2,15),(3,11),(4,3)
my answer: c) (1,-3),(3,5),(5,11),(7,18)
Answer a)
x1 = 1 , y1= - 2
x2 = 3 , y2 = 1
x3 = 5 , y3= 4
x4 = 7 , y4 = 7
x2 - x1 = 3 - 1 = 2
x3 - x2 = 5 - 3 = 2
x4 - x3 = 7 - 3 = 2
y2 - y1 = 1 - ( - 2 ) = 1 + 2 = 3
y3 - y2 = 4 - 1 = 3
y4 - y3 = 7 - 4 = 3
Numerically, y increases by 3 units for every 2 unit increase of x.
correct
http://www.wolframalpha.com/input/?i=plot+%281%2C-3%29%2C%283%2C5%29%2C%285%2C11%29%2C%287%2C18%29
Reiny
c)
isn't correct answer
In w o l f r a m a l p h a . c o m
type:
interpolate (1,-3),(3,5),(5,11),(7,18)
That is a cubic polynomial.
and
x4 - x3 = 7 - 5 = 2
sorry, did not register the "linear" part, and concentrated on the "increasing"
actually I think it is a),
the slope between any two points is 3/2
all points satisfy the equation
3x-2y=7
http://www.wolframalpha.com/input/?i=interpolate+%281%2C-2%29%2C%283%2C1%29%2C%285%2C4%29%2C%287%2C7%29+
Bosnian was right in his first post.
(think I will have a third cup of coffee to wake up)
To determine which data set represents an increasing linear function, we need to examine the relationship between the x-coordinates (input) and the y-coordinates (output).
An increasing linear function is one in which the y-coordinate increases as the x-coordinate increases.
Let's go through each option to check:
a) (1,-2),(3,1),(5,4),(7,7)
Here, as the x-coordinate increases from 1 to 3, the y-coordinate increases from -2 to 1. So far, it seems to be increasing. But when the x-coordinate increases from 3 to 5, the y-coordinate increases from 1 to 4, which is smaller than the previous increase. Hence, this data set does not represent an increasing linear function.
b) (1,1),(2,0),(3,-1),(4,-2)
In this set, as the x-coordinate increases, the y-coordinate decreases. Therefore, it does not represent an increasing linear function.
c) (1,-3),(3,5),(5,11),(7,18)
Here, as the x-coordinate increases from 1 to 3, the y-coordinate increases from -3 to 5. Continuing further, as the x-coordinate increases from 3 to 5, the y-coordinate increases from 5 to 11. This pattern shows consistent positive increments in the y-coordinate as the x-coordinate increases, which indicates an increasing linear function. Therefore, this data set does represent an increasing linear function.
d) (1,17),(2,15),(3,11),(4,3)
In this set, the y-coordinate decreases as the x-coordinate increases, which means it does not represent an increasing linear function.
So, based on our analysis, your answer is correct. Option c) (1,-3),(3,5),(5,11),(7,18) is the data set that represents an increasing linear function.