What is the relationship between the rate of change and the slope

Find the equation of the lines parallel and perpendicular to the line 5x+2y=12 through the point (-2,3)

muminat

Answer:

The equation of line parallel to given line and passing through points ( - 2 , 3 ) is 5 x + 2 y + 4 = 0

The equation of line perpendicular to given line and passing through points ( - 2 , 3 ) is 2 x - 5 y + 19 = 0

Step-by-step explanation:

Given equation of line as :

5 x + 2 y = 12

or, 2 y = - 5 x + 12

or , y = $\frac{-5}{2}$ x + $\frac{12}{2}$

Or, y = $\frac{-5}{2}$ x + 6

∵ Standard equation of line is give as

y = m x + c

Where m is the slope of line and c is the y-intercept

Now, comparing given line equation with standard eq

So, The slope of the given line = m = $\frac{-5}{2}$

Again,

The other line if passing through the points (- 2 , 3 ) And is parallel to given line

So, for parallel lines condition , the slope of both lines are equal

Let The slope of other line = M

So, M = m = $\frac{-5}{2}$

∴ The equation of line with slope M and passing through points ( -2 , 3) is

y = M x + c

Now , satisfying the points

So, 3 = $\frac{-5}{2}$ × ( - 2 ) + c

or, 3 = $\frac{10}{2}$ + c

Or, 3 = 5 + c

∴ c = 3 - 5 = - 2

c = - 2

So, The equation of line with slope $\frac{-5}{2}$ and passing through points ( -2 , 3)

y = $\frac{-5}{2}$ x - 2

or, 2 y = - 5 x - 4

I.e 5 x + 2 y + 4 = 0

Similarly

The other line if passing through the points (- 2 , 3 ) And is perpendicular to given line

So, for perpendicular lines condition,the products of slope of both lines = - 1

Let The slope of other line = M'

So, M' × m = - 1

Or, M' × $\frac{-5}{2}$ = - 1

Or, M' = $\frac{-1}{\frac{-5}{2}}$

Or, M' = $\frac{2}{5}$

∴ The equation of line with slope M and passing through points ( -2 , 3) is

y = M' x + c'

Now , satisfying the points

So, 3 = $\frac{2}{5}$ × ( - 2 ) + c'

or, 3 = $\frac{- 4}{5}$ + c'

Or, 3 × 5 = - 4 + 5× c'

∴ 5 c' = 15 + 4

or, 5 c' = 19

Or, c' = $\frac{19}{5}$

So, The equation of line with slope $\frac{2}{5}$ and passing through points ( -2 , 3)

y = $\frac{2}{5}$ x + $\frac{19}{5}$

y = $\frac{2 x + 19}{5}$

Or, 5 y = 2 x + 19

Or, 2 x - 5 y + 19 = 0

Hence The equation of line parallel to given line and passing through points ( - 2 , 3 ) is 5 x + 2 y + 4 = 0

And The equation of line perpendicular to given line and passing through points ( - 2 , 3 ) is 2 x - 5 y + 19 = 0

Answer

4 0

3 years ago

Please help Find the perimeter of the following shape, rounded to the nearest tenth

KATRIN_1 [288]

Answer:

19.1

Step-by-step explanation:

i took the testttttt

5 0

3 years ago

Find the value of -12 + 8 -(-9)

Tasya [4]

-12 + 8 - (-9) = 5
Therefore the value of -12 + 8 - (-9) is 5.

7 0

3 years ago

What % of the first 15 whole numbers have exactly 4 distinct whole number divisors? (1, 2, 3, and 6 are the four distinct diviso

skelet666 [1.2K]

When a natural number is expressed as a product of two other natural numbers, those other numbers are factors of the original number. For example, two factors of 12 are 3 and 4, because 3 • 4 = 12.

When one number can be divided by another number with no remainder, we say the first number is divisible by the other number. For example, 20 is divisible by 4 (). If a number is divisible by another number, it is also a multiple of that number. For example, 20 is divisible by 4, so 20 is a multiple of 4.

A Prime Number can be divided evenly only by 1 or itself.
And it must be a whole number greater than 1.

Example: 7 can only be divided evenly by 1 or 7, so it is a prime number.

But 6 can be divided evenly by 1, 2, 3 and 6 so it is NOT a prime number (it is a composite number).

Let me explain ...

Some whole numbers can be divided up evenly, and some can't!

Example:

6 can be divided evenly by 2, or by 3:

6 = 2 × 3

Like this:

ordivided into 2 groups divided into 3 groups

But 7 cannot be divided up evenly:

And we give them names:

When a number can be divided up evenly it is a Composite NumberWhen a number can not be divided up evenly it is a Prime Number

So 6 is Composite, but 7 is Prime.

Many mathematical operations have an inverse, or opposite, operation. Subtraction is the opposite of addition, division is the inverse of multiplication, and so on. Squaring, which we learned about in a previous lesson (exponents), has an inverse too, called "finding the square root." Remember, the square of a number is that number times itself. The perfect squares are the squares of the whole numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 …

The square root of a number, n, written

is the number that gives n when multiplied by itself. For example,

because 10 x 10 = 100

Examples

Here are the square roots of all the perfect squares from 1 to 100.

Finding square roots of of numbers that aren't perfect squares without a calculator

1. Estimate - first, get as close as you can by finding two perfect square roots your number is between.

2. Divide - divide your number by one of those square roots.

3. Average - take the average of the result of step 2 and the root.

4. Use the result of step 3 to repeat steps 2 and 3 until you have a number that is accurate enough for you.

Example: Calculate the square root of 10 () to 2 decimal places.

1. Find the two perfect square numbers it lies between.

Solution:
32 = 9 and 42 = 16, so lies between 3 and 4.

2. Divide 10 by 3. 10/3 = 3.33 (you can round off your answer)

3. Average 3.33 and 3. (3.33 + 3)/2 = 3.1667

Repeat step 2: 10/3.1667 = 3.1579
Repeat step 3: Average 3.1579 and 3.1667. (3.1579 + 3.1667)/2 = 3.1623

Try the answer --> Is 3.1623 squared equal to 10? 3.1623 x 3.1623 = 10.0001

If this is accurate enough for you, you can stop! Otherwise, you can repeat steps 2 and 3.

Note: There are a number of ways to calculate square roots without a calculator. This is only one of them.

4 0

3 years ago

Read 2 more answers

Evaluate f(x) = 2x +3 for f(4) a-11 b-8 c-4 d-3

Scrat [10]

Answer:

the answer is a-11

Step-by-step explanation:

f(x)=2x+3

f(4)=2(4)+3

f(4)=8+3

f(4)=11

5 0

3 years ago