Ask question

Ask question

All categories

3 years ago

7

When given two data points, how would you use this information to create a linear equation? How would you create a linear equati

on if you were given an initial value and a rate of change? Use examples of your own to explain the process.

1 answer:

marta [7]3 years ago

7 0

Given two (different) points, there is only one line passing through them. So, the linear equation modelling your dataset would be the line passing through the two data points.

In order to find the line, you can use the following equaiton: given two points $A = (A_x, A_y)\ ,B=(B_x,B_y)$ , the line passing through them is given by

$\dfrac{y-A_y}{B_y-A_y} = \dfrac{x-A_x}{B_x-A_x}$

For example, given the points $A = (1,1)$ and $B = (5,7)$ , you have

$\dfrac{y-1}{7-1} = \dfrac{x-1}{5-1} \iff \dfrac{y-1}{6} = \dfrac{x-1}{4} \iff 4(y-1) = 6(x-1)$

Now, if you want, you can rearrange this in the form

$4y-4 = 6x-6 \iff 4y = 6x-2 \iff y = \dfrac{3x}{2} - \dfrac{1}{2}$

You might be interested in

Casey uses some of his savings on batting practice. the cost of renting a batting cage for 1 hour is $6. he rents a cage for 9 h

sammy [17]

It 54 thank you welcome you

5 0

3 years ago

Select all that apply.

kkurt [141]

Sample space, The counting Principle and, a table can be used

7 0

3 years ago

4. a) A ping pong ball has a 75% rebound ratio. When you drop it from a height of k feet, it bounces and bounces endlessly. If t

Klio2033 [76]

First part of question:

Find the general term that represents the situation in terms of k.

The general term for geometric series is:

$a_{n}=a_{1}r^{n-1}$

$a_{1}$ = the first term of the series

$r$ = the geometric ratio

$a_{1}$ would represent the height at which the ball is first dropped. Therefore:

$a_{1} = k$

We also know that the ball has a rebound ratio of 75%, meaning that the ball only bounces 75% of its original height every time it bounces. This appears to be our geometric ratio. Therefore:

$r=\frac{3}{4}$

Our general term would be:

$a_{n}=a_{1}r^{n-1}$

$a_{n}=k(\frac{3}{4}) ^{n-1}$

Second part of question:

If the ball dropped from a height of 235ft, determine the highest height achieved by the ball after six bounces.

$k$ represents the initial height:

$k = 235\ ft$

$n$ represents the number of times the ball bounces:

$n = 6$

Plugging this back into our general term of the geometric series:

$a_{n}=k(\frac{3}{4}) ^{n-1}$

$a_{n}=235(\frac{3}{4}) ^{6-1}$

$a_{n}=235(\frac{3}{4}) ^{5}$

$a_{n}=55.8\ ft$

$a_{n}$ represents the highest height of the ball after 6 bounces.

Third part of question:

If the ball dropped from a height of 235ft, find the total distance traveled by the ball when it strikes the ground for the 12th time. 

This would be easier to solve if we have a general term for the <em>sum </em>of a geometric series, which is:

$S_{n}=\frac{a_{1}(1-r^{n})}{1-r}$

We already know these variables:

$a_{1}= k = 235\ ft$

$r=\frac{3}{4}$

$n = 12$

Therefore:

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{1-\frac{3}{4} }$

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{\frac{1}{4} }$

$S_{n}=(4)(235)(1-\frac{3}{4} ^{12})$

$S_{n}=910.22\ ft$

8 0

3 years ago

Which of these equations is shown on this graph?

AlekseyPX

<em><u>should be G : y=2x+1</u></em>

4 0

3 years ago

Read 2 more answers

Jose asks his friends to guess the higher of two grades he received on his math tests. He gives them two hints. The difference o

denis23 [38]

Option D. 96 is the correct answer.

Explanation:

Let the higher grade be = x

Let the lower grade be = y

As given, The difference of the two grades is 16

$x-y=16$ or $x=16+y$ .... (1)

The sum of one-eighth of the higher grade and one-half of the lower grade is 52.

$\frac{1x}{8}+\frac{1y}{2}=52$ ... (2)

Putting the value of x=16+y in equation (2)

$\frac{16+y}{8}+\frac{y}{2}=52$

$\frac{16+y+4y}{8}=52$

$\frac{16+5y}{8}=52$

$16+5y=416$

$5y=400$

$y=80$

As x=16+y

x=16+80 = 96

Hence, higher grade is 96.

8 0

3 years ago