Question

analyzing steps to write a linear equation
a 5-minute international call costs $2.15 and a 12-minute call costs $3.06. the work shows how to write an equation where x represents the number of minutes, and y represents the total cost of an international call. analyze the steps of the work to determine if the equation is correct.

1. point 1: (5, 2.15), point 2: (12, 3.06)
2. ( m = \frac{12 - 5}{3.06 - 2.15} = \frac{7}{0.91} approx 7.69 )
3. ( 5 = 2.15(7.69) + b )

( b approx -11.54 )

1. ( y = 7.69x - 11.54 )

in which step did emilia make an error?

• in step 2, she substituted the x values for y and the y values for x.
• in step 3, she didn’t use an x and y from the same coordinate pair.
• in step 4, emilia solved for the wrong variable.
• emilia did not make an error

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \), not \( \frac{x_2 - x_1}{y_2 - y_1} \).

Step2: Analyze Emilia's step 2

Emilia used \( m=\frac{12 - 5}{3.06 - 2.15} \), which swaps \( x \) and \( y \) values. She should have used \( m=\frac{3.06 - 2.15}{12 - 5} \). So in step 2, she substituted \( x \) values for \( y \) and \( y \) values for \( x \).

Answer:

In step 2, she substituted the \( x \) values for \( y \) and the \( y \) values for \( x \).