Linear Equation Study Guide

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Algebra I Chapter 5 Study Guide Writing Linear Equations

Name ________________
Due: Tuesday, January 17 (Exam week)

100 points

Writing Linear Equations in a Variety of Forms
Using given information about a __________, you can write an ________________of the line in _____________ different forms. Complete the chart:

Form (Name)

Equation
• •

Important information
The slope of the line is ____. The __ - ___________ of the line is _____. The slope of the line is _____. The line passes through ( ______, ______ ) A, B, and C are __________ numbers. A and B are not both ___________.

Slope – Intercept

Point – Slope

• •

Standard

• •

Try a few (Page 345 – 347) Write an equation in Slope – Intercept Form:

Algebra I

Study Guide Chapter 5

lopeWrite an equation in Slope-Intercept Form that passes through the given point and has the given slope m. 8. (23, 21); m = 4 y= m= x= b= 9) (– 2, 1), m = 1 y= m= x= b= 10) (8, –4) m = – 3 y= m= x= b=

Write an equation in Point-Slope Form that passes through the given points. oint11) (4, 7) (5, 1) 12) (9, 22) (23, 2) 13) (8, 28) (23, 22)

(Hint: you need slope)

(Hint: you need slope)

(Hint: you need slope)

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Algebra I

Study Guide Chapter 5

Write an equation in Standard Form of the line that has the given characteristics.

Hint for #15 & #16 You’ll need to write one form of the equation and transform it … think of our charts … and, see the example above the problem in the book … page 347 15) Slope: 24; passes through (22, 7)

16) Passes through (21, 25) and (3, 7)

Keep going!
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Algebra I

Study Guide Chapter 5

Problems Using Linear Models (Equations) to Solve Problems
You can write a linear equation that ______________ a situation involving a _____________rate of change (_____________). Analyzing given information helps you choose a _______________ model.

If this is what you know …
Constant rate of change (____) and Initial value (_____) Constant rate of change (____) and One data pair ( _____, _____ ) Two data pairs (x1, y1)* and (x2, y2)* and the fact that the Rate of Change (____) is constant

… then use this equation form

*You can use these to find _______________ (m)
The sum (or difference) of two variable quantities ( ____ and ____ ) is constant

Master the Word Problem! (Page 345, #7)
You have a $25 gift card for a bagel shop. A bagel costs $1.25. 1. Write an equation that gives the amount (in dollars) that remains on the card as a function of the total number of bagels you have purchased so far. 2. How much money is on the card after you buy 2 bagels?

Keep going … a few more examples to do!
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Algebra I

Study Guide Chapter 5

Remember! Life is a Word Problem … so get good at it!
Page 346 – 7: 14 & 17
A bus leaves at 10 A.M. to take students on a field trip to a historic site. At 10:25 A.M., the bus is 100 miles from the site. At 11:15 A.M., the bus is 65 miles from the site. The bus travels at a constant speed. 1. Write an equation in point-slope form that relates the distance (in miles) from the site and the time (in minutes) after 10:00 A.M. 2. How far is the bus from the site at 11:30 A.M.?

You are buying ribbon to make costumes for a school play. Organza ribbon costs $.07 per yard. Satin ribbon costs $.04 per yard. 1. Write an equation to model the possible combinations of yards of organza ribbon and yards of satin ribbon you can buy for $5. 2. List several possible combinations.

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Algebra I

Study Guide Chapter 5

perpendicular Finally, our friends, parallel & perpendicular … We’ve discussed Parallel lines before …. let’s add Perpendicular (two lines that form a ______________ angle).

Type
Parallel

Important information
Same ______________ (m) Different y - ________________ (b)

Examples

Perpendicular

Slopes are _______________ reciprocals Y – intercept can be the ___________

Try a few (page 347)
Hint: Since they give you a point...
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