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3 years ago

How do I write this in Point Slope, Slope-Intercept, and in Standard form. Thanks for the help!

Mathematics

1 answer:

AnnZ [28]3 years ago

6 0

Point slope form: y - y1 = m (x - x1)
-------------------------------------------------

first you need to find the slope(m) by using the slope formula (seen below)

y2 - y1
m= ---------
x2 - x1

9 - 15
m= ---------
1 - (-2)

-6
m= --------- = -2
3

then choose either one of the coordinates you'd like and plug it in.

Im gonna use (-2, 15)

(y - 15) = -2 (x - (-2))
or
(y - 15) = -2 (x + 2)

slope intercept form: y = mx + b
-----------------------------------------------

you can use the slope formula to find that the slope(m) is -2

y = -2x + b

you can then plug in a coordinate to find b (the y-intercept)

I'll use (-2,15)

15 = -2(-2) +b
15 = 4 + b
-4 -4
---------
11 = b

in conclusion:

the slope(m) = -2

when (-2,15) is used
x = -2
y = 15
b = 11

standard form: ax + by = c
----------------------------------------

using the same coordinate (-2,15)

-2a + 15b = c

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4 years ago

Find the reduced row echelon form of the following matrices and then give the solution to the system that is represented by the

GaryK [48]

Answer:

Reduced Row Echelon:

$\left[\begin{array}{cccc}1&1/2&0&0\\0&1&7/4&0\\0&0&1&-4\end{array}\right]$

Solution to the system:

$x_3=-4\\x_2=-\frac{7}{4}x_3=7\\x_1=-\frac{1}{2}x_2=-\frac{7}{2}$

Reduced Row Echelon:

$\left[\begin{array}{cccc}4&3&0&7\\0&0&2&-17\\0&0&2&-17\end{array}\right]$

Solution to the system:

$x_3=-\frac{17}{2}\\x_1=\frac{7-3x_2}{4}$

x_2 is a free variable, meaning that it has infinite possibilities and therefore the system has infinite number of solutions.

Step-by-step explanation:

To find the reduced row echelon form of the matrices, let's use the Gaussian-Jordan elimination process, which consists of taking the matrix and performing a series of row operations. For notation, R_i will be the transformed column, and r_i the unchanged one.

a) $\left[\begin{array}{cccc}0&4&7&0\\2&1&0&0\\0&3&1&-4\end{array}\right]$

Step by step operations:

1. Reorder the rows, interchange Row 1 with Row 2, then apply the next operations on the new rows:

$R_1=\frac{1}{2}r_1\\R_2=\frac{1}{4}r_2$

Resulting matrix:

$\left[\begin{array}{cccc}1&1/2&0&0\\0&1&7/4&0\\0&3&1&-4\end{array}\right]$

2. Set the first row to 1

$R_3=-3r_2+r_3$

Resulting matrix:

$\left[\begin{array}{cccc}1&1/2&0&0\\0&1&7/4&0\\0&0&1&-4\end{array}\right]$

3. Write the system of equations:

$x_1+\frac{1}{2}x_2=0\\x_2+\frac{7}{4}x_3=0\\x_3=-4$

Now you have the reduced row echelon matrix and can solve the equations, bottom to top, x_1 is column 1, x_2 column 2 and x_3 column 3:

$x_3=-4\\x_2=-\frac{7}{4}x_3=7\\x_1=-\frac{1}{2}x_2=-\frac{7}{2}$

$\left[\begin{array}{cccc}4&3&0&7\\8&6&2&-3\\4&3&2&-10\end{array}\right]$

1. $R_2=-2r_1+r_2\\R_3=-r_1+r_3$

Resulting matrix:

$\left[\begin{array}{cccc}4&3&0&7\\0&0&2&-17\\0&0&2&-17\end{array}\right]$

2. Write the system of equations:

$4x_1+3x_2=7\\2x_3=-17$

Now you have the reduced row echelon matrix and can solve the equations, bottom to top, x_1 is column 1, x_2 column 2 and x_3 column 3:

$x_3=-\frac{17}{2}\\x_1=\frac{7-3x_2}{4}$

x_2 is a free variable, meaning that it has infinite possibilities and therefore the system has infinite number of solutions.

7 0

3 years ago

Really need helpllllll!!!!!

kirza4 [7]

Answer:

The relationship of the number of months and the total amount paid is proportional for both Hanks and Lynn.

Step-by-step explanation:

Let us divide the equation into 2 parts.

Hanks

Hank paid $2000 up front when he bought the car and he pays $200 every month. Therefore, the total amount paid (y) and the number of month (x)can be expressed as follows.

Let

x = number of month

y = total amount paid

y = 2000 + 200x

The relationship between amount paid and the number of months is proportional

Lynn

She did not paid anything upfront but she paid $275 every month. Therefore,

x = number of month

y = total amount paid

y = 275x

This relationship between amount paid and number of month is directly proportional

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3 years ago

SOMEONE PLEASE HELP ME FAST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Mademuasel [1]

Answer:

The answer is B!

I hope this helps!

p.s. have any more questions? Post the question and comment the link below!

Ciao!

♥, Sadie

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3 years ago

Read 2 more answers

Ben believe the orioles will win only 40% of their games this year if they play 160 games how many games does Ben predict they w

aleksandr82 [10.1K]

The number of games Ben predict Orioles will win this year is 64 games

<h3>How to find percentage?</h3>

Percentage of games Ben believe the orioles will win = 40%
Number of games Orioles played = 160

Number of games Ben predict they will win = 40% of 160

= 40/100 × 160

= 0.4 × 160

= 64

Therefore, the total number of games Ben predict they will win is 64 games

Learn more about percentage:

brainly.com/question/843074

#SPJ1

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2 years ago