Question

"Juan earns 7 per hour plus 20 per week making picture frames.

Without graphing the function, determine the slope. Write your answer as a fraction in simplest form."

A) 7/20
B) 20/7
C) 27/7
D) 7/27

Answer 1

Step-by-step explanation:

you must have skipped and/or mistyped something in your problem definition, because none of the given 4 answer options is correct for the given problem.

the slope is always the ratio

y coordinate difference / x coordinate difference

when going from one point on the line to another.

when going in steps of single units on the x-axis (like in our case hour by hour), the x circuses difference is always 1. and all we need to is checking how much the y-value changes for each step.

as it is described, Juan earns 7 money units more for every additional working hour.

so, the slope is then 7/1 = 7

the function corresponding to the description text above is

week_income(x) = f(x) = 7x + 20

x being the number of hours worked.

and 20 is the fixed part he is getting no matter how many hours he worked (even 0).

as you can see, the answer options are not fitting.

you have to use my explanation to find the correct answer.

what could the answer options mean:

A) 7/20 : he earns 7 for every 20 hours work.

B) 20/7 : he earns 20 for every 7 hours of work.

C) 27/7 : he earns 27 for every 7 hours of work.

D) 7/27 : he earns 7 for every 27 hours of work

again, there is nothing in the problem definition you gave us, that even hints to work hour units as multiples of 7, 20, or 27 work hours.

Answer 2

Juan's earnings are represented by a linear function with a slope of $7 for each hour worked. The correct answer to the slope of Juan's earnings function is 7, which in this context, indicates his hourly wage.

Step-by-step explanation:

The question involves understanding the slope of a linear function that represents Juan's earnings. Juan earns a fixed amount of $20 per week plus $7 for each hour he works on making picture frames. The linear equation representing Juan's earnings per week can be written as y = 7x + 20, where y represents the total earnings and x is the number of hours worked. The term '7' represents the slope of this function, which signifies that Juan earns $7 for each additional hour of work. The slope is a rate of change, so it's simply the coefficient of the x term in the equation.