Using Linear Equations to Solve Real World Problems!

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Presentation transcript:

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. y=10x+25 y=15x+35 y=20x+1,300 Identify the slope (“m”) Click on the tasks to write a linear equation. Plug in the “m” and “b” to y=mx+b Identify the y-intercept (“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. 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. Eddie: y=4.99x + 39.99 Luis: y=3.99x + 49.99 Birthday: y=.75x + 12.50 Get Well: y=.50x + 9.70 Identify the slope (“m”) Click on the tasks to write a system of linear equations. Plug in the “m” and “b” to y=mx+b Identify the y-intercept (“b”)

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 y = 299x + 500 Guatemala Driving Solutions y = 307 x + 400 Xela Cars 14,852 = 299(48) + 500 Guatemala Driving Solutions 14,215= 307(45) + 400 Identify the slope (“m”) Plug in the “x” to y=mx+b Plug in the “m” and “b” to y=mx+b Identify the solution. Click on the tasks to write a system of linear equations. Identify the y-intercept (“b”) Identify the independent variable (“x”)

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!!!