Question

I NEED HELP ASAP !!!!!!!!!!!!!!!!!!!!

1.)Which table of values corresponds to the graph below?
*use picture 1 and 2

2.)Water from a leaking faucet is dripping into a cylindrical cup. The height of water in inches, y, after x hours is graphed below.
*USE PICTURE 3
Which describes the pattern of the data in the graph?
The water level increases by 1 inch each hour.
The water level increases by 2 inches each hour.
The water level increases by a factor of 1/2 each hour.
The water level increases by a factor of 2 each hour.

Answer 1

1. A table of values that corresponds to the graph above is: A. table 1.

2. A statement that describes the pattern of the data in the graph is: B. The water level increases by 2 inches each hour.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

`Slope(m)=(y_2-y_1)/(x_2-x_1)`

Part 1.

For the slope of the graph through the points (0, 0) and (3, 1), we have;

Slope(m) = (1 - 0)/(3 - 0)

Slope(m) = 1/3.

For table 1, we have;

Slope(m) = (0 + 1)/(0 + 3)

Slope(m) = 1/3.

For table 2, we have;

Slope(m) = (0 + 3)/(0 + 1)

Slope(m) = 3.

For table 3, we have;

Slope(m) = (0 + 1)/(0 + 1)

Slope(m) = 1.

For table 4, we have;

Slope(m) = (0 + 1)/(0 + 1)

Slope(m) = 1.

Part 2.

Since the graph represents a proportional relationship and passes through the origin (0, 0), the constant of proportionality can be calculated as follows;

Constant of proportionality, k = y/x

Constant of proportionality, k = 2/1 = 4/2 = 6/3

Constant of proportionality, k = 2 inches per hour.

In conclusion, the water level increases by a height of 2 inches each hour.

Answer 2

Question 1). table 1

Question 2). Option B

Explanation:

Question 1). If we analyse graph 1 we find a straight line of which we have to find the equation first.

Since the equation of any line is represented by y = mx + c

where m = slope of the line

c = y- intercept

Graph 1 shows line has no y-intercept (passing through origin) so c = 0

and the equation will be y = mx

Now slope m =
`(y-y')/(x-x')`

In graph 1 line is passing through two points (3, 1) and (0, 0).

Therefore m =
`(1-0)/(3-0)=(1)/(3)`

Finally equation of the line is
`y=(1)/(3)x`

or x - 3y = 0

Now we plug in the values of x and y from graph 2, table 1

For (-3, -1)

-3 - (3)(-1) = -3 + 3 = 0

So table 1 is the answer.

Question 2). In this question we have to describe the pattern showing the relation between x and y.

In other words we have to find the slope of the line which describes flow of water y in x hours.

Slope =
`(y-y')/(x-x')`

Here the line is passing through two points (0, 0) and (1, 2)

By putting the values in the formula of slope

`m= (2-0)/(1-0)=2`

So water level in the cup is increasing by 2 inches per hour.

Option B. is the answer.