Question

1. compare the two functions to determine which has a negative slope. (2 pts.) function 1: devin has $40.00. he spends $3.00 each week purchasing new pencils for math class. let y be the amount of money devin has remaining after x number of weeks. function 2: james has 11 baseball cards at the beginning of the month. he purchases 3 more cards each day. let y represent the total amount of cards james has after x number of days. function 1 / function 2 how i know: ?

Explanation:

Step1: Define Function 1 equation

Devin starts with $40 and spends $3 weekly. The remaining money $y$ after $x$ weeks is:
$y = 40 - 3x$

Step2: Identify Function 1 slope

In the form $y=mx+b$, $m$ is slope. For Function 1, $m = -3$.

Step3: Define Function 2 equation

James starts with 11 cards and gains 3 daily. Total cards $y$ after $x$ days is:
$y = 11 + 3x$

Step4: Identify Function 2 slope

In the form $y=mx+b$, $m$ is slope. For Function 2, $m = 3$.

Step5: Compare slopes

$-3$ is negative, $3$ is positive.

Answer:

Function 1
How I know: Function 1 has a slope of $-3$, which is negative, while Function 2 has a positive slope of $3$.