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lys-0071 [83]
3 years ago
8

Sum 1 Teach Me Linear Relations Your Boy Doesn’t Understand It;)

Mathematics
1 answer:
Juliette [100K]3 years ago
7 0

Answer:

A linear equation is an equation for a straight line

These are all linear equations:

yes   y = 2x + 1

yes   5x = 6 + 3y

yes   y/2 = 3 − x

Let us look more closely at one example:

Example: y = 2x + 1 is a linear equation:

line on a graph

The graph of y = 2x+1 is a straight line

 

When x increases, y increases twice as fast, so we need 2x

When x is 0, y is already 1. So +1 is also needed

And so: y = 2x + 1

Here are some example values:

x y = 2x + 1

-1 y = 2 × (-1) + 1 = -1

0 y = 2 × 0 + 1 = 1

1 y = 2 × 1 + 1 = 3

2 y = 2 × 2 + 1 = 5

Check for yourself that those points are part of the line above!

Different Forms

There are many ways of writing linear equations, but they usually have constants (like "2" or "c") and must have simple variables (like "x" or "y").

Examples: These are linear equations:

yes   y = 3x − 6

yes   y − 2 = 3(x + 1)

yes   y + 2x − 2 = 0

yes   5x = 6

yes   y/2 = 3

But the variables (like "x" or "y") in Linear Equations do NOT have:

Exponents (like the 2 in x2)

Square roots, cube roots, etc

Examples: These are NOT linear equations:

not   y2 − 2 = 0

not   3√x − y = 6

not   x3/2 = 16

Slope-Intercept Form

The most common form is the slope-intercept equation of a straight line:

y=mx+b graph

Equation of a Straight Line y=mx+b

Slope (or Gradient) Y Intercept

 

Example: y = 2x + 1

Slope: m = 2

Intercept: b = 1

Animation    

Play With It !

You can see the effect of different values of m and b at Explore the Straight Line Graph

Point-Slope Form

Another common one is the Point-Slope Form of the equation of a straight line:

y − y1 = m(x − x1)

 Point-Slope Form

Example: y − 3 = (¼)(x − 2)

It is in the form y − y1 = m(x − x1) where:

y1 = 3

m = ¼

x1 = 2

General Form

And there is also the General Form of the equation of a straight line:

Ax + By + C = 0

(A and B cannot both be 0)

Example: 3x + 2y − 4 = 0

It is in the form Ax + By + C = 0 where:

A = 3

B = 2

C = −4

There are other, less common forms as well.

As a Function

Sometimes a linear equation is written as a function, with f(x) instead of y:

y = 2x − 3

f(x) = 2x − 3

These are the same!

And functions are not always written using f(x):

y = 2x − 3

w(u) = 2u − 3

h(z) = 2z − 3

These are also the same!

The Identity Function

There is a special linear function called the "Identity Function":

f(x) = x

And here is its graph:

Identity Function

It makes a 45° (its slope is 1)

It is called "Identity" because what comes out is identical to what goes in:

In Out

0 0

5 5

−2 −2

...etc ...etc

Constant Functions

Another special type of linear function is the Constant Function ... it is a horizontal line:

Constant Function

f(x) = C

No matter what value of "x", f(x) is always equal to some constant value.

Using Linear Equations

You may like to read some of the things you can do with lines:

Finding the Midpoint of a Line Segment

Finding Parallel and Perpendicular Lines

Finding the Equation of a Line from 2 Points

Source: https://www.mathsisfun.com/algebra/linear-equations.html

Step-by-step explanation:

heeyyyy hmu ;) <333333333

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10 x 23 x 4 divided by 54 x 4
barxatty [35]

Answer: roughly 4.2593

Step-by-step explanation:

920/216

put the equation through a calculator

approx. 4.2593

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Find how much should be invested to have $12,000 in 11 months at 6.1% simple interest.
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Answer:

6654.54

Step-by-step explanation:

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3 years ago
Hey i need help!!!!<br> What do the following two equations represent?<br> *6x-15y=15<br> *y=2/5x-1
Rina8888 [55]

The given two equations represent that 6x-15y=15  is equal to y=2/5x-1 And they have the same slope 2/5.

<h3>What is equation?</h3>

Equations are logical statements in mathematics that are denoted by an equals (=) sign and two algebraic expressions on either side of it. It is demonstrated that the expressions on the left and right are equal to one another.

All mathematical equations start with LHS = RHS (left hand side = right hand side). To find the value of an unknown variable, or unknown quantity, you can solve equations. If the statement does not contain a "equal to" symbol, it is not an equation. It will be considered as an expression.

We have been asked to find the value of x and y in 6x-15y=15 and y=2/5x-1

Let solve for y = 2/5x-1

in  6x - 15y = 15

⇒ 6x - 15(2/5x-1) = 15

⇒ 6x - 6x  + 15 = 15

⇒ 15 = 15

⇒ This mans they have slope

⇒ 6x - 15y = 15 in y-intercept form

⇒ 15y = 6x - 15

⇒ 15y = 6x - 15

⇒ y = (6x - 15)15

⇒ y = 2/5x - 1

Thus, 6x-15y=15  is equal to y=2/5x-1 And they have the same slope 2/5.

Learn more about equation

brainly.com/question/2972832

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Classify each number as rational or irrational.
zimovet [89]
0.167\ -\ rational\\\\\dfrac{2}{9}\ -\ rational\\\\\pi\ -\ irrational\\\\\sqrt{225}=15\ -\ rational
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Consider △RST and △RYX.
anastassius [24]

Answer:

B. \frac{RY}{RS} = \frac{RX}{RT} = \frac{XY}{TS}, must be true.

Step-by-step explanation:

Similar figures are figures whose angles and sides are similar with respect to a definite ratio when compared.

From the given question, note that ΔRXY is within ΔRST. Given that the two triangles are similar, then their sides can be compare in a form of ratio as:

\frac{RY}{RS} = \frac{RX}{RT} = \frac{XY}{TS}

Therefore by comparing the length of sides of the triangles, option B must be true.

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