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A graph shows the number of texts, numbered 10 to 100, on the x-axis, and the total cost in dollars, numbered 3 to 27, on the y-axis. A straight red line with a positive slope, labeled Emilia, begins at (0, 10), and a straight blue line with a positive slope, labeled Hiroto, begins at (0, 20). Both lines intersect at point (50, 22.5).
Hiroto’s texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia’s plan costs $10 per month and $0.25 per text. Using the graph below, which statement is true?

Hiroto’s plan costs more than Emilia’s plan when more than 50 texts are sent.
Both plans cost the same when 22 texts are sent.
Emilia’s plan costs more than Hiroto’s plan when more than 22 texts are sent.
Both plans cost the same when 50 texts are sent

Answer :

The correct statement regarding the linear functions is given by:

Both plans cost the same when 50 texts are sent.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

For this problem, we consider the flat fee as the intercept and the cost per message as the slope, hence the functions are given by:

  • E(x) = 10 + 0.25x.
  • H(x) = 20 + 0.05x.

Initially, Hiroto costs are higher, then after the threshold, Emilia's costs are higher. The threshold is given by:

E(x) = H(x)

10 + 0.25x = 20 + 0.05x

0.2x = 10.

x = 100/2

x = 50.

Hence the correct statement is given by:

Both plans cost the same when 50 texts are sent.

More can be learned about linear functions at https://brainly.com/question/24808124

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