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3 years ago

This graph represents a linear function. Which equation is represented by this graph?

Mathematics

1 answer:

lisabon 2012 [21]3 years ago

3 0

Answer:

Answer is A

Step-by-step explanation:

» Consider two points plotted on the line;

(3, 0) and (0, -2)

» General equation of a line has an expression in format of;

${ \rm{y = mx + c}}$

m is the slope
c is the y-intercept

» Finding the slope [m] :

${ \rm{slope = \frac{y_{2} - y _{1}}{x _{2} - x _{1} } }} \\$

• But remember from the points or coordinates we fetched out of the graph;

${ \tt{y_{2} = - 2}} \: \mid \: { \tt{y_{1} = 0}} \\ { \tt{x_{2} =0 }} \: \mid \: { \tt{x_{1} = 3}}$

Therefore, lets feed in the formular:

${ \tt{m = \frac{ {}^{ - } 2 - 0}{0 - 3} = \frac{ - 2}{ - 3} }} \\ \\ { \boxed{ \tt{m = \frac{2}{3} }}}$

» Finding y-intercept [c] :

☑ REMEMBER: y = mx + c

• Consider point (0, -2)

${ \tt{y = mx + c}} \\ { \tt{ - 2 = ( \frac{2}{3} \times 0) + c}} \\ \\ { \boxed{ \tt{ \: c = - 2 \: }}}$

» Arrange the equation:

Equation is y = ⅔x - 2

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3 years ago

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Write a quadratic equation with the given roots. Write the equation in the form of ax^2+bx+c=0 where a b and c are integers

Bas_tet [7]

You haven't provided the required roots, but I can tell you how to do this kind of exercises in general.

If the $x^2$ coefficient is 1, i.e. the equation is written like $x^2+bx+c=0$ , then you can say the following about the coefficients b and c:

$b$ is the opposite of the sum of the roots
$c$ is the multiplication of the roots.

So, for example, if we want an equation whose roots are 4 and -2, we have:

$4+(-2) = 4-2 = 2 \implies b = -2$
$4 \cdot (-2) = -8 \implies c = -8$

So, the equation is $x^2-2x-8=0$

If your roots are rational, you can work like this: suppose you want an equation with roots 3/4 and 1/2. You have:

$\dfrac{3}{4}+\dfrac{1}{2} = \dfrac{3}{4}+\dfrac{2}{4} = \dfrac{5}{4} \implies b = -\dfrac{5}{4}$
$\dfrac{3}{4} \cdot \dfrac{1}{2} = \dfrac{3}{8} \implies c = \dfrac{3}{8}$

And so the equation is

$x^2 - \dfrac{5}{4} + \dfrac{3}{8} = 0$

In order to have integer coefficients, you can multiply both sides of the equation by 8:

$8x^2 - 10 + 3 = 0$

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3 years ago

Determine whether each sequence is arithmetic. If so, identify the common difference.

-Dominant- [34]

Answer:

Options 1 and 4 are arithmetic

Step-by-step explanation:

Arithmetic means that you are adding or subtracting a number in a sequence.

For option 1, we are adding 2 every time.

-3 + 2 = -1 -1 + 2 = 1 1 + 2 = 3

For option 4, we are subtracting 7 every time.

32 - 7 = 25 25 - 7 = 18 18 - 7 = 11

Option 2 is geometric. Geometric means you are multiplying or dividing by a number in a sequence.

2 * 3 = 6 6 * 3 = 18 18 * 3 = 54

Option 3 is actually quadratic. This is similar to a arithmetic, except instead, the amount added to the number is multiplied by 2 every time.

1 + 2 = 3 (2 + 2 = 4) 3 + 4 = 7 (4 + 4 = 8) 7 + 8 = 15

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3 years ago

Giving brainleyest

sweet-ann [11.9K]

Answer:

Answer is 6....this is 100 % correct answer

<h3>Hope this helps u.... ^_^❤️</h3>

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3 years ago

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PLEASE HELP ASAP ITS DUE SOON AND I NEED THE ANSWER RN! SHOW YOUR WORK ILL GIVE BRAINLIEST

IceJOKER [234]

Answer:

(12, -6)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Terms/Coefficients
Coordinates (x, y)
Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

-4x = y - 42

x = 18 + y

Step 2: Solve for y

Substitute in x: -4(18 + y) = y - 42
Distribute -4: -72 - 4y = y - 42
[Addition Property of Equality] Add 4y on both sides: -72 = 5y - 42
[Addition Property of Equality] Add 42 on both sides: -30 = 5y
[Division Property of Equality] Divide 5 on both sides: -6 = y
Rewrite/Rearrange: y = -6

Step 3: Solve for x

Define original equation: x = 18 + y
Substitute in y: x = 18 - 6
Subtract: x = 12

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3 years ago