How do you find the equation of a line with guassian elimination given two points?

  The solution is similar to the 2-point form of the equation for a line:

  y = (y2 -y1)/(x2 -x1)·x + (y1) -(x1)(y2 -y1)/(x2 -x1)

Step-by-step explanation:

Using the two points, write two equations in the unknowns of the equation of the line.

For example, you can use the equation ...

  y = mx + b

Then for the points (x1, y1) and (x2, y2) you have two equations in m and b:

  b + (x1)m = (y1)

  b + (x2)m = (y2)

The corresponding augmented matrix for this system is ...

____

The "b" variable can be eliminated by subtracting the first equation from the second. This puts a 0 in row 2 column 1 of the matrix, per Gaussian Elimination.

  0 + (x2 -x1)m = (y2 -y1)

Dividing by the value in row 2 column 2 gives you the value of m:

  m = (y2 -y1)/(x2 -x1)

This value can be substituted into either equation to find the value of b.

  b = (y1) -(x1)(y2 -y1)/(x2 -x1) . . . . . substituting for m in the first equation

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

see below

step-by-step explanation:

7.   there are 10 data points in the set.   the middle point is between 5 and 6.   the middle point in the top half is 8   and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term   point 8 = 100   point 3 = 88

iqr = 100-88 = 12

final   point 8 = 93   point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6.   b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical .   there is an outlier for the males that skews the data

5.   the   iqr is a better measure of spread for the movies and basketball games.   since the basketball game has an outlier, we do not want to use standard deviation for measurement.  

3.   the exam median is much higher than the class median.   the median line is farther to the right on the exams

2.   there is no way to tell what the means are from the box and whisker plots.