Answer:
[tex]140+6x=462-10x[/tex]
Step-by-step explanation:
Let
x ----> the number of weeks
y ---> amount of money in the bank
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope or unit rate
b is the y-intercept or initial value
Katherine
The slope or unit rate is equal to
[tex]m=\$6\ per\ week[/tex]
The y-intercept or initial value is equal to
[tex]b=\$140[/tex]
The linear equation is equal to
[tex]y=6x+140[/tex] ----> equation A
Abbie
The slope or unit rate is equal to
[tex]m=-\$10\ per\ week[/tex] ----> is negative because is a decreasing function
The y-intercept or initial value is equal to
[tex]b=\$462[/tex]
The linear equation is equal to
[tex]y=-10x+462[/tex] ----> equation B
Equate equation A and equation B
[tex]6x+140=-10x+462[/tex]
Rewrite the terms
[tex]140+6x=462-10x[/tex]
