An advertiser goes to a printer and is charged $73 for 100 copies of one flyer and $82 for 400 copies of a similar flyer. Assuming the cost for a printing job is represented by a linear equation, find the equation (in slope-intercept form) that describes the cost y of a printing job if x is the number of Copies made. Also, write a sentence describing what the slope of the equation represents in this situation.

Question

02-10-2019
Mathematics

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An advertiser goes to a printer and is charged $73 for 100 copies of one flyer and $82 for 400 copies of a similar flyer. Assuming the cost for a printing job is represented by a linear equation, find the equation (in slope-intercept form) that describes the cost y of a printing job if x is the number of Copies made. Also, write a sentence describing what the slope of the equation represents in this situation.

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valetta valetta · Answer 1 · 2019-10-04T09:46:56+02:00

Answer:

y = 0.03x + 70

Slope here represents the variation in the charges with the change in the number of flyers

Positive slope means that the cost is increasing with increase in number of flyers

Step-by-step explanation:

Given:

for 100 copies advertiser is charged = $73

For 400 copies advertiser is charged = $82

Now,

here the charge is a function of number of flyers

we have the general line equation for a linear relationship as:

y = mx + c

here m is the slope

c is the constant

for the first case we have

y = $73

x = 100

thus,

73 = 100m + c ...........(1)

for the second case, we have

y = $82

x = 400

thus,

82 = 400m + c ...........(2)

subtracting (1) from (2)

82 = 400m + c

- ( 73 = 100m + c )

==================

9 = 300m + 0

or

m = 0.03

substituting the value of slope in equation (1)

73 = 100 × 0.03 + c

73 = 3 + c

or

c = 70

Hence,

the equation is y = 0.03x + 70

here y is amount charged and x are the number of flyers.

Slope here represents the variation in the charges with the change in the number of flyers

Positive slope means that the cost is increasing with increase in number of flyers