Question

this is a 2-page document!
slope-intercept applications ($y = mx + b$)

1. a music app charges $2 to download the app plus $1.29 per song downloaded. write and solve a linear equation to find the total cost to download 30 songs.
2. carly has already written 35 pages of a novel. she plans to write 12 additional pages per month until she is finished. write and solve a linear equation to find the total number of pages written at 5 months.
3. the late fee for library books is $2.00 plus 15¢ each day for a book that is late. if maria’s fee for a late book was $3.20, write and solve a linear equation to find how many days late the book was.
4. a group of mountain climbers begin an expedition with 250 pounds of food. they plan to eat a total of 12 pounds of food per day. write and solve a linear equation to find the number of days their food will last.
5. an airplane at 30,100 feet above the ground begins descending at the rate of 2,150 feet per minute. write and solve a linear equation to find how many minutes it will take the plane to reach the ground.

Explanation:

Problem 1

Step1: Define variables and equation

Let \( x \) be the number of songs, \( y \) be total cost. The equation is \( y = 1.29x + 2 \) (slope \( m = 1.29 \), y - intercept \( b = 2 \)).

Step2: Substitute \( x = 30 \)

Substitute \( x = 30 \) into \( y = 1.29x + 2 \): \( y = 1.29(30)+2 \).

Step3: Calculate

\( 1.29\times30 = 38.7 \), then \( y = 38.7 + 2 = 40.7 \).

Step1: Define variables and equation

Let \( x \) be months, \( y \) be total pages. Equation: \( y = 12x + 35 \) (slope \( m = 12 \), y - intercept \( b = 35 \)).

Step2: Substitute \( x = 5 \)

Substitute \( x = 5 \) into \( y = 12x + 35 \): \( y = 12(5)+35 \).

Step3: Calculate

\( 12\times5 = 60 \), then \( y = 60 + 35 = 95 \).

Step1: Define variables and equation

Let \( x \) be days, \( y \) be total fee. \( 15\) cents \( = 0.15\) dollars, so equation: \( y = 0.15x + 2 \). We know \( y = 3.20 \), so \( 3.20 = 0.15x + 2 \).

Step2: Solve for \( x \)

Subtract 2 from both sides: \( 3.20 - 2 = 0.15x \), \( 1.20 = 0.15x \).

Step3: Divide

Divide both sides by 0.15: \( x=\frac{1.20}{0.15}=8 \).

Answer:

The total cost is \$40.70.

Problem 2