Question

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writing a linear equation from a word problem
tables are one way to represent linear functions. you can also find linear functions in real - world situations where something changes at a constant rate. in this activity, youll learn to write linear equations from word problems. follow your teachers instructions to complete the example below.

1. malcolm’s checking account has a minimum balance of $1,500 and charges a $14 fee each month the account is below that minimum. after buying textbooks, malcolm’s balance is $1,357.

a. create a table showing malcolm’s balance, y, after x months if he makes no deposits or withdrawals.

b. initial value: _______
c. slope: _______
d. write an equation representing malcolm’s balance.
e. find y when x = 12. what does that mean in this scenario?

Explanation:

Step1: Define initial values

Initial balance $y_0 = 1357$, monthly fee = $14$

Step2: Build the table

Calculate $y = 1357 - 14x$ for $x=0,1,2,3,4,5$

• $x=0$: $y=1357-14(0)=1357$
• $x=1$: $y=1357-14(1)=1343$
• $x=2$: $y=1357-14(2)=1329$
• $x=3$: $y=1357-14(3)=1315$
• $x=4$: $y=1357-14(4)=1301$
• $x=5$: $y=1357-14(5)=1287$

Step3: Identify initial value

Initial value is balance at $x=0$: $1357$

Step4: Identify slope

Slope = monthly rate of change: $-14$

Step5: Write linear equation

Use $y = mx + b$, $m=-14$, $b=1357$: $y = -14x + 1357$

Step6: Calculate $y$ at $x=12$

Substitute $x=12$ into equation:
$y = -14(12) + 1357 = -168 + 1357 = 1189$

Answer:

a.

x	y
1	1343
2	1329
3	1315
4	1301
5	1287

b. $\$1357$

c. $-14$

d. $y = -14x + 1357$

e. $\$1189$; This is Malcolm's account balance after 12 months of being below the minimum balance, with no deposits or withdrawals.