Forms of a Line.

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Presentation transcript:

Forms of a Line

The Murchison Middle School NJHS is selling t-shirts and caps to raise money for their DC trip. They earn a profit of $5 per shirt and $10 per cap. Find 5 pairs of numbers for shirt and cap sales that will allow the students to make exactly $600 profit.

The Murchison Middle School NJHS is selling t-shirts and caps to raise money for their DC trip. They earn a profit of $5 per shirt and $10 per cap. The values you found can be expressed as an ordered pair (s, c). Plot these ordered pairs on a grid, with shirts as x and caps as y.

The Murchison Middle School NJHS is selling t-shirts and caps to raise money for their DC trip. They earn a profit of $5 per shirt and $10 per cap. Write the equation of the line on your graph in slope intercept form, y=mx+b. What do “m” and “b” mean in this problem?

The Murchison Middle School NJHS is selling t-shirts and caps to raise money for their DC trip. They earn a profit of $5 per shirt and $10 per cap. Write the equation of the line on your graph in point-slope form, y-y1 = m(x-x1). What do “m” and “(x1, y1)” mean in this problem?

The Murchison Middle School NJHS is selling t-shirts and caps to raise money for their DC trip. They earn a profit of $5 per shirt and $10 per cap. A more meaningful equation for this problem would be: 5s + 10c = 600. What do the 5, 10, and 600 mean in this problem situation? How can you use this to find other solutions?

Notes Standard Form: Ax + By = C Rule 1: A is always positive Rule 2: A, B, and C are always whole numbers. A, B, and C are not anything “algebraic” but are important information in the problem. Standard form does not show slope intercepts points

Try a similar example… Students are selling calendars for $3 each and posters for $2 each. They want to sell a total of $100 worth of products. Write an equation using p, for posters, and c for calendars. Use your equation to answer the question: How many posters must they sell if they have already sold 20 calendars?

Try a similar example… Eric walks 80 meters per minute and runs 200 meters per minute. He wants to cover a distance of 1600 meters by both walking and running. If he walks for 10 minutes, how many minutes must he run? Write the equation first. What info is NOT needed for the equation? Answer the question. Where do you find the info needed to answer the question?

Other types of Standard Form Problems Two rates, find totals Two totals, find rates Money Perimeter Totals Ratios

Try a TWO TOTALS example… Courtney bought 7 bags of chips and 12 packages of hot dogs. She spent $27. How much were the chips if the hot dog packages were $0.50? Write the equation. Answer the question.

Try a MONEY example… Neema saves quarters and dimes. She has a total of $1.65. How many dimes does she have if she has 5 quarters? Write the equation. Answer the question.

Try a PERIMETER example… A pool has a perimeter of 500 meters. What is the length if the width is 100 meters? Write the equation. Answer the question.

Try a TOTALS example… Luanne recycles cans and bottles. She has a total of 225 recyclables. How many cans does she have if she has 127 bottles? Write the equation. Answer the question.

Try a RATIO example… The ratio of desks to tables in the building is 2 to 15. How many tables are there if there are 34 desks? Write the equation. Answer the question.