I believe the answer would be B
Theo ran 3K in 9.6 minutes:
9.6 divided by 3 = 1.2 munutes
3 divided by 3 = 1k
1k = 1.2 minutes.
Estaban ran 5k in 13.5 minutes:
13.5 divided by 5 = 2.7 minutes
5 divided by 5 = 1k
1k = 2.7 munutes
Tetsuo ran 10k in 31.9 minutes:
31.9 divided by 10 = 3.19 munites
10 divided by 10 = 1k
1k = 3.19 minutes
Answer: Theo Ran the Fastest and all the writing above is the resoning.
This graph has a horizontal asymptote so it is an exponential graph. It also passes through two points (0,-2) and (1,3). The horizontal asymptote is at y=-3.
The unchanged exponential equation is y=a(b)^x +k
For exponential equations, k is always equal to the horizontal asymptote, so k=-3.
You can check this with the ordered pair (0,-2). After that plug in the other ordered pair, (1,3).
This gives you 3=a(b)^1 or 3=ab. If you know the base the answer is simple as you just solve for a.
If you don't know the base at this point you have to sort of guess. For example, let's say both a and b are whole numbers. In that case b would have to be 3, as it can't be 1 since then the answer never changes, and a is 1. Then choose an x-value and not exact corresponding y-value. In this case x=-1 and y= a bit less than -2.75. Plug in the values to your "final" equation of y=(3)^x -3.
So -2.75=(3^-1)-3.
3^-1 is 1/3, 1/3-3 is -8/3 or -2.6667 which is pretty close to -2.75. So we can say the final equation is y=3^x -3.
Hope this helps! It's a lot easier to solve problems like these given either more points which you can use system of equations with, or with a given base or slope.
Answer:
C. (0,-3)
Step-by-step explanation:
y = 2x - 3
We only need to focus on "- 3" because it represents "b" of the equation y = mx + b.
Since it is a y intercept, the coordinate must be at the y axis.
So,
x = 0
y = -3
(0,-3)
