706.3.7 Translate between verbal and symbolic representations of real-world phenomena involving linear equations.

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Presentation transcript:

Translate between verbal and symbolic representations of real-world phenomena involving linear equations.

In real life, situations where we can use algebra are often presented as verbal descriptions. Fortunately, in verbal descriptions, there are key words that help us know how to translate the verbal descriptions into algebraic symbols.

All linear functions can be written in the form y=mx + b where y is the dependent variable, m is the slope, x is the independent variable, and b is the y-intercept.

Key Words for slope: per for every every of multiplied by for each each apiece

Other common usage for slope: hourly pay weekly pay monthly pay annual pay Example ~ $10.50 an hour

Some key words that indicate y-intercept: fixed rate starting point one-time fee down payment initial payment fixed cost start-up cost hook-up fee

Often, you will see two numbers in the text and have to decide which is the slope and which is the y-intercept. Let ’ s look at a sample problem to demonstrate.

Lee took a cab to the zoo. The company charges a fixed rate of $4.95 for pick- up and 40 cents for each additional 0.1 mile. Which equation best represents the cost y for the ride, if the trip was x tenths of a mile? a.0.4x – 4.95 b.O.4x c.4.95x d.4.95x – 0.4 What is the slope?

Lee took a cab to the zoo. The company charges a fixed rate of $4.95 for pick-up and 40 cents for each additional 0.1 mile. Which equation best represents the cost y for the ride, if the trip was x tenths of a mile? a.0.4x – 4.95 b.O.4x c.4.95x d.4.95x – 0.4 Look for the key slope words.

Lee took a cab to the zoo. The company charges a fixed rate of $4.95 for pick-up and 40 cents for each additional 0.1 mile. Which equation best represents the cost y for the ride, if the trip was x tenths of a mile? a.0.4x – 4.95 b.O.4x c.4.95x d.4.95x – 0.4 What is the y-intercept?

The amount A that the Hernandez family spends in n weeks for groceries at a local food club includes $5 for the initial registration fee and $37 each week for a box of groceries. Which equation describes the relationship between A and n? a.45(n + 37) b.45n + 37 c.37n + 45 d.37(n + 45) What is the slope?

Reggie reserved a hotel meeting room for a presentation. The hotel required an initial payment of $100 plus $5 per person attending the event. Which equation best represents the total fee y that the hotel will charge if x people attend the presentation? a.100x + 5 b.100x – 5 c.5x d.5x - 100

Summary: 1.Identify the slope by looking for key words like per, for every, each, etc. 2. Make sure that the slope is next to x, or the independent variable. 3. Look for the other number, the y- intercept, to be by itself, added to or subtracted from the x-term.

Now, let ’ s practice!