Chapter 5: Writing Linear Equations Sections 1-4 Name Algebra Notes Using Linear Equations to Solve Problems Slope-Intercept Point Slope Standard Form y = mx + b y- y 1 = m ( x = x 1 ) Ax + By = C So, we ve done all of this practice writing equations in different forms for what???? Great question! Equations can actually be used to and solve, whether figuring out your pay or determining how to send a rocket to the moon. Let s try a few using Slope Intercept: y = mx + b A recording studio charges musicians an initial fee of $50 to record an album. Studio time costs an additional $35 per hour. Write an equation that gives the total cost of an album as a function of studio time (in hours). 1. Re-word the problem in to a statement: The total cost 2. Translate your words in to math you ve got your equation! 3. What would it cost for 10 hours of studio time? y = m = x = b = Which variable is the: total cost? number of hours?
Here s another: A gym charges $25 per month after an initial membership fee. A member has paid a total of $250 after 6 months. Write an equation that gives the total cost of a gym membership as a function of the length of membership (in months). 1. Re-word the problem: The total cost 2. Translate your words in to math you ve got your equation! y = m = x = b = 3. Find the total cost of membership after 4 months. Which variable is the: total cost? number of months? IN SUMMARY: Use Slope Intercept Form. When the total ( ) is a result of a change ( ) in another quantity ( ). Look for words like to find your slope ( ). The starting point, or an initial fee or cost, is your y intercept ( ). Page 2 of 6
Let s try one using Point Slope Form: y y 1 = m ( x x 1 ) You are designing a sticker to advertise your band. A company charges $225 for the first 1000 stickers and $80 for each additional 1000 stickers. Write an equation that gives the total cost (in dollars) of stickers as a function of the number (in thousands) of stickers ordered. Find the cost of 9000 stickers. 1. Identify the rate of change and a data pair. Let C be the cost (in dollars) and S be the number of stickers (in thousands). Rate of Change = (S, C) = This is your slope! (m) Think of this as your (x 1, y 1 ) 2. Write an equation using point-slope form. 3. Rewrite the equation in slopeintercept form so that cost is a function of the number of stickers. Get by itself for Slope Intercept: Which variable is the: total cost? number of stickers? IN SUMMARY: Use Point - Slope Form. When you have a problem that involves a constant rate of change your, and a data pair your. Key words? can help find slope ( ). The (, ) point is the data combination the problem gives you. Page 3 of 6
Let s try one using Standard Form: Ax + By = C Your class is taking a trip to the Library of Congress. You can travel in small and large vans. A small van holds 8 people and a large van holds 12 people. Your class could fill 15 small vans and 2 large vans. Write an equation in standard form that models the possible combinations of small vans and large vans that your class could fill. Write the equation you need to find C. 1. Label your two variables and their corresponding rate of change. van ( ) holds ( ) To find C, plug in the number of each van you could fill for x and y: van ( ) holds ( ) Write your equation. 2. Use the equation to find your intercepts and use them to make a graph: x 0 y 0 3. Find points that meet at integer coordinates. 4. List these ordered pairs these are your possible combinations for large and small vans! IN SUMMARY: Use Standard Form When you have a problem that involves a of two types of quantities. Page 4 of 6
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