Download Using Linear Equations to Solve Real World Problems!

Using Linear Equations to Solve
Real World Problems!
When using linear equations to solve real world
problems you must first learn to identify the slope
and the y-intercept of the situation. The slope is
always a rate and you should recognize that it occurs
often (ex. monthly, daily, per…, each…, every…, etc.).
The y-intercept represents a one time fee or a fixed
rate (ex. down payment). Then you plug these values
into the slope-intercept form of the equation of a line
“y=mx+b”. After you’ve done this you can then solve
the problem by plugging in the “x” or “y” value given.
Writing a Linear Equation
• Write a linear equation to model the following situations:
– Jeremy buys an iPod for a down payment of $25 and a $10 monthly payment.
– Lidia pays $35 to get acrylic nails put on and then pays $15 per month to get them filled.
– Derek gets paid a salary of $1,300 plus $20 a night in tips.
Identify
the
slope
(“m”)
Plug in the “m”
and “b” to
Identify the
y-intercept
(“b”)
y=mx+b
Writing a System of Linear Equations
• Write a system of linear equations for the following examples:
– Luis and Eddie are buying new light systems to decorate their cars. Eddie finds one that
costs $39.99 and requires new batteries that cost $4.99 each month. Luis finds one that
costs $49.99 and requires new batteries that cost $3.99 each month.
Eddie: y=4.99x + 39.99
Luis: y=3.99x + 49.99
– Nancy and Diana sell balloons for special occasions. The Happy Birthday package costs
$12.50 plus $0.75 per candy bar. The Get Well package costs $9.70 plus $0.50 per piece
of candy.
Birthday: y=.75x + 12.50
Identify
the
slope
(“m”)
Plug in the “m”
and “b” to
Identify the
y-intercept
(“b”)
y=mx+b
Get Well: y=.50x + 9.70
Using a System of Linear Equations to
Solve Problems
• Write a system of linear equations to solve the following problem:
– Brenda and Moises decide to buy a new car and they need to figure out which
dealership will give them the best deal. Xela Cars offers them a down payment price of
$500 and a monthly fee of $299 for 48 months. While Guatemala Driving Solutions
offers a down payment of $400 and a monthly fee of $307 for 45 months. Which
dealership should they buy their car from?
Xela Cars
Cars 14,852
= 299(48)
Guatemala Driving
Driving Solutions
307(45)
+ 400
Xela
y = 299x
+ 500 + 500Guatemala
Solutions14,215=
y = 307
x + 400
Identify
the
slope
(“m”)
Plug in the “m”
and “b” to
y=mx+b
Identify the
y-intercept
(“b”)
Identify the
independent
variable (“x”)
Plug in the
“x” to
y=mx+b
Identify the
solution.
Yay Hooray!!!
• You can now use linear equations to solve real
world problems. Brenda and Moises thank
you for helping them find the most affordable
car!!!