hey there my name is Kaeleigh in this lesson we will build linear functions
from word problems let's get started
here's our first example it says Sarah is writing a story
she writes five pages every day and she has already written fifteen pages which
of the following represents the number of pages y written after X days so
what we're trying to do here is write a linear function which normally looks
like y equals MX plus B or y equals B plus MX either version is fine so we're
trying to find the number of pages Y so we can write y equals and then we know
that she's already written fifteen pages so that's what she starts with and
that's what our B here represents so we can write fifteen plus we know X is the
number of days so what is a rate that she does that's every day or per day
she writes five pages every day so she writes five so that's her rate pages per
day times the number of days X so our answer should look like y equals fifteen
plus 5x which looks like this one right here
nice work let's try another one all right our next one says William is
washing dishes he washes two plates every minute and he has already washed
12 plates which of the following represents the number of plates Y washed
after X minutes so again for reference we're trying to write a linear equation
which typically takes a form like that so we're trying to find the number of
plates why so why is our number of plates after X minutes they'll be no
that William has already washed 12 plates so we can write that first and
now we need our X is in minutes so we need to find a rate that's per minute or
every minute and it says he washes two plates every minute so that's our rate
two plates every minute times the number of minutes would give us his total
number of dishes so it will look like y equals 12 plus 2x watches down there
great job let's give one more example to try together before you do these on your
own okay this one says the level of water H
in a tank is 9 feet it decreases every hour by 8 inches which of the following
represents the level of water H measured in inches depending on the number of
hours T so we are still looking for our linear relationship here but it looks
like they've changed up our variables so we have an H and a T now so H is the
level of water in the tank that's what we're looking for so we're gonna convert
our Y to an H is going to equal to still a rate but our rate is times the number
of hours T plus our starting value B okay so we can say H is equal to what is
our starting value 9 feet all right 9 feet there and now we need to find our
rate our rate says decreases every hour by 8 inches so decreases here that tells
us it's going down so we're going 9 feet - our rate of 8 inches per hour times T
the number of hours that passes but they said we need to measure everything in
inches so we need to convert this 9 feet here to inches
so it'll be H is equal to there's 12 inches in every foot so 9 times 12 108
inches minus 8 inches per hour times the number of hours so our linear
relationship looks like that a great job so now you will get to play the game and
do the online quizzes to practice building linear functions
I'd recommend having y equals MX plus B written down when you go through these
on your own so that you remember that M is your rate and B is your starting
value and keep an eye out for if it's decreasing or increasing and if you need
to change units at any time great job have fun and remember to
always be clever