HiSET: Math help » Algebraic ideas » features and function notation » sensible relationship between two quantities

A restaurant sets the prices of its dishes using the complying with function:

Price = (Cost the Ingredients) + (40% of the expense of Ingredients) + 5

where all quantities are in U.S. Dollars. 

If the expense of ingredients because that a steak dish is $14, what will the restaurant set the price the the steak dish at?


Explanation:

The price that the food is a function of a solitary variable, the expense of the ingredients. One means to conceptualize the trouble is by reasoning of it in duty notation. Allow

*
 be the change representing the cost of the ingredients. Allow
*
 be a function of the price of ingredients giving the price of the dish. Then, we deserve to turn

"Price = (Cost of Ingredients) + (40% of the price of Ingredients) + 5"

into a consistent equation through recognizable parts. Replace "Price" v

*
 and change "cost that ingredients" v the variable
*
.

You are watching: What is a relationship between two quantities

*

Simplify through combining choose terms (

*
 and
*
) come obtain:

*

The expense of ingredients for the steak food is $14, so instead of 14 because that

*
.

*
 

All that"s left is to compute the answer:

*

So, the steak dish will have actually a price of $24.60.


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Example inquiry #2 : useful Relationship in between Two amounts


*


The plot shows the graphs the five different equations. Using shape and also location, determine which graphed line corresponds to the equation 

*
.


Possible Answers:

Line B


Line A


Line D


Line E


Line C


Correct answer:

Line B


Explanation:

The power of

*
 and
*
 are both 1, therefore this is a straight equation of order 1. Therefore, the graph need to be a straight line. We can get rid of A and E, since neither are straight lines. 

The equation is offered in the slope-intercept form,

*
, whereby
*
 stands because that the slope of the line and also
*
 stands because that the line"s y-intercept. Because
*
, the coefficient that x, is positive here, we are searching for a line that goes upwards. We can get rid of D because it walk downwards, and therefore has a an unfavorable slope.

In the provided equation, the constant

*
, which to represent the y-intercept, is additionally positive. Therefore, the heat we are looking for likewise must intersect the y-axis at a confident value. The graph C appears to crossing the y-axis in ~ a an unfavorable value, conversely, the graph B appears to intersect the y-axis at a hopeful value. Therefore, B is the matching graph.

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