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julia-pushkina [17]
3 years ago
9

Which statement best explains whether the table represents a linear or nonlinear function?

Mathematics
1 answer:
Marta_Voda [28]3 years ago
7 0

Answer: A.) It is a linear function because there is a constant rate of change in both the input and output values.

============================================================

Explanation:

Note how x is decreasing by 3 each time

  • -2-3 = -5
  • -5-3 = -8
  • -8-3 = -11

At the same time, y is also decreasing by 3 each time

  • 7-3 = 4
  • 4-3 = 1
  • 1-3 = -2

This means we have a linear function. We have,

slope = (change in y)/(change in x)

slope = (-3)/(-3)

slope = 1

Recall that slope is another term for rate of change, so a constant slope means we have a constant rate of change.

----------------

Another way to find the slope is to pick any two points from the table and use the slope formula

m = (y2 - y1)/(x2 - x1)

You should find that any two points you pick will lead to a slope of 1. I recommend you try out all possible pairs to help convince yourself the slope is 1.

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Which is the graph of the line LaTeX: y-2=3\left(x-1\right)y − 2 = 3 ( x − 1 )?
andreyandreev [35.5K]

Answer:

D.

Step-by-step explanation:

The equation given takes the point-slope form which is, y - b = m(x - a). Where,

(a, b) = (x, y) coordinates of a point on the line.

m = slope of the line .

To find which graph has a line equation of y - 2 = 3(x - 1), look for the points which will give you something almost exactly as the equation if you substitute their values into y - b = m(x - a).

Let's consider option D.

We have a given point (1, 2). a = 1, b = 2.

Substitute these into y - b = m(x - a)

We have:

y - (2) = m(x - (1))

y - 2 = m(x - 1)

As you can see, this looks almost exactly as

y - 2 = 3(x - 1).

If you want to be certain that option D is the answer, find m by using the coordinates of any other point on the line and plug into y - 2 = m(x - 1) to find m:

In graph D, let's take the points (0, -1)

-1 - 2 = m(0 - 1)

-3 = m(-1)

-3 = -m

Divide both sides by -1

3 = m

m = 3.

Therefore, option D is the graph of the line y - 2 = 3(x - 1).

3 0
3 years ago
Fine the equation of the line: slope = -2 y-intercept= 5
soldi70 [24.7K]
Using the y=mx+b format
M= slope
B= y-intercept
All you need to do, since both m and b are given us to plug them in! You should commit “y=mx+b” to memory, it’ll help you a ton!
y = -2x+5
3 0
2 years ago
You are selling candy bars for the school to
Strike441 [17]

Answer:

200 bars

Step-by-step explanation:

$300 - $50 = the amount of money you still need, $250

250 dollars/$1.25 per bar = 200 bars you need to sell to get 300 dollars

7 0
4 years ago
At a race track you have the opportunity to buy a ticket that requires you to pick the first and second place horses in the firs
rewona [7]

Answer:

4032 different tickets are possible.

Step-by-step explanation:

Given : At a race track you have the opportunity to buy a ticket that requires you to pick the first and second place horses in the first two races. If the first race runs 9 horses and the second runs 8.

To find : How many different tickets are possible ?

Solution :

In the first race there are 9 ways to pick the winner for first and second place.

Number of ways for first place - ^9C_1=9

Number of ways for second place - ^8C_1=8

In the second race there are 8 ways to pick the winner for first and second place.

Number of ways for first place - ^8C_1=8

Number of ways for second place - ^7C_1=7

Total number of different tickets are possible is

n=9\times 8\times 8\times 7

n=4032

Therefore, 4032 different tickets are possible.

8 0
3 years ago
college algebra - please help The half-life for thorium-227 is 18.72 days. The amount A (in grams) of thorium-227 after t days f
Andreyy89

Answer:

t= 24.75 days

Step-by-step explanation:

Here A(t) is the amount of the element that remains after some time. So they tell us that find the time it takes to basically have 4 grams remaining so A(t) = 4

4 = 10 * 0.5 ^ (t/18.72)

0.4= 0.5 ^ (t/18.72)

t= 24.75 days

Answer should make sense because half life is around 18 days which means to go from 10 g to 5g would be somewhere around 18 days but we are going to 4 g so it takes more days

6 0
4 years ago
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