Question

the table shows the percentage of battery life, y, that remains x hours after a cell phone is turned on.
cell phone battery life
hours, x | percentage remaining, y
0 | 100
1 | 75
2 | 50
3 | 25
4 | 0
based on the information in the table, which equation can be used to model the relationship between x and y?
a ( y = -4x + 25 )
b ( y = 25x + 100 )
c ( y = 25x + 4 )
d ( y = -25x + 100 )

Explanation:

Step1: Determine the slope

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using the points \((0, 100)\) and \((1, 75)\), we get \( m=\frac{75 - 100}{1 - 0}=\frac{- 25}{1}=-25 \).

Step2: Determine the y - intercept

The y - intercept \( b \) is the value of \( y \) when \( x = 0 \). From the table, when \( x = 0 \), \( y = 100 \), so \( b = 100 \).

Step3: Write the equation

The slope - intercept form of a line is \( y=mx + b \). Substituting \( m=-25 \) and \( b = 100 \) into the equation, we get \( y=-25x + 100 \).

Answer:

D. \( y=-25x + 100 \)