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3 years ago

The graph of a proportional relationship will always be a straight line that passes through the origin. Why?

Mathematics

1 answer:

sashaice [31]3 years ago

5 0

Answer:

Being proportional between two entities, refers to the 'Constant of Proportionality' that would be fixed between them which establishes a relationship between them when multiplied or divided.

If we considered it on a graph, the 'Constant Of Proportionality' may take any real values between the coordinate pairs x and y [x,y]. As even 0 is a real number, it will surely be a constant of proportionality when multiplied since its product would result in itself (0). Hence, both x and y turns 0.

As the coordinates of the origin are always (0,0), the graph (Or the slope) would surely pass through the origin.

Example :

If we consider a graph such that x=y.

And if we multiply or divide any real number (a) between them.

ax=ay

As a is a variable, and can take the value of 0, the graph can pass through the origin as x and y nullify becoming the coordinates of the origin.

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Answer:

0.75 or 3/4

Step-by-step explanation:

f(-2) = 3•2^-2

f(-2) = 3•0.25

f(-2) = 0.75 or 3/4

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3 years ago

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4 years ago

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3 years ago

on a piece of paper graph y=(x+2)(x-3) then determine which answer choice best matches the graph you drew. Provide an explanatio

ioda

Answer:

option C

Step-by-step explanation:

Given :-

y = (x + 2)( x -3)

And we need to tell which graph best matches the graph we drew. Firstly let's convert it into a quadratic equation by opening and simplifying the brackets.

$:\implies$ y = ( x + 2) ( x - 3)

$:\implies$ y = x ( x - 3)+2( x - 3)

$:\implies$ y = x² - 3x + 2x -6

$:\implies$ y = x² - x - 6

Now plot its graph. For that refer to attachment.

Things we can interpret :-

The constant in the equation is -6. So the graph will cut y axis 6 units below the X axis . At (-6,0)
From the given options , option C matches the above point .

Therefore the correct option is (C) .