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Chapter 5 Notes A2

Short Answer

1. Ch. 5.1: Write Linear Equations in Slope-Intercept Form

Example 1: Write the equation of the line with a slope of −2 and a y-intercept of 5.

Example 2: Write the equation of the line shown.

Example 3: Write the equation of the line shown,

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Example 4: Write the equation for the linear function f with the values f(0) = 5 and f(4) = 17.

f(0) = -2, f(8) = 4

f(-3) = 6, f(0) = 5

Example 5: A recording studio charges musicians an initial fee of $50 to record an album. Studio time costs and additional $35 per hour.

a. Write an equation thatgives the total cost of an album as a function of studio time in hours.

b. Find the total cost of recording an album that takes 10 hours of studio time.

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2. Ch 5.2: Use Linear Equations in Slope-Intercept form

Writing an Equation of a line in Slope-Intercept Form.

Step 1: Identify the slope m. You can use the slope fromula to calculate the slope if you know two points on the line.

Step 2: Find the y-intercept. You can substitute the slope and the coordinates of a point (x,y) on the line in y = mx + b. Then solve for b.

Step 3: Write an equation using y = mx + b.

Example 1: Write the equation of a line that passes through the point (−1,3) and has a slope of -4.

Write the equation of a line that passes through the point (6,3) and has a slope of 2.

Example 2: Write the equation of the line that passes through (-2,5) and (2,-1).

Write the equation of the line that passes through (1, -2) and (-5, 4).

Example 3: Write an equation for the function which has the values f(4) = 9 and f(-4) = -7.

Write an equation for the function which has the values f(-2) = 10 and f(4) = -2.

Example 4: Your gym membership cost $33 per month after an initail membership fee. You paid a total of $228 after 6 months. Write an equation that gives the total cost as a function of the length of your gym membership. Find the cost after 9 months.

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Example 5: In BMX racing, racers purchase a one year membership to a track. The also pay an entry fee for each race at that track. One racer paid a total of $125 after 5 races. A second racer paid a total of $170 after 8 races. How much does the track membership cost? What is the entry fee per race?

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3. Ch 5.3: Write Linear Equations in Point-Slope Form

________________________: y − y1 = m(x − x1). m = slope. x and y are unknown points on the

line (never chage). x1 and y1 are known points.

Example 1: Write the equation in point slope form of the line that passes through the point (4,-3) and has a slope of 2.

Example 2: Graph the equation y + 2 = 23

(x − 3)

Example 3: Write the equation in point-slope form of the line shown.

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Write an equation in point slope form of a line that passes through the point (2,3) and (4,4)

Example 4: You are designing 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.

Example 5: The table shows the cost of visiting a working ranch for one day and night for different numbers of people. Can the situation be modeled by a linear equation? If so, write an equation that gives the cost as a function of the number of people in the group.

# People 4 6 8 10 12Cost $ 250 350 450 550 650

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4. Ch 5.4: Write Linear Equations in Standard Form

___________________________: Ax + By = C

Example 1: Write two equations in Standard form that are equivalent to 2x − 6y = 4.

Example 2: Write an equation in standard from of the line shown.

Guided Practice:1. Write two equations in standard from that are equivalent to x − y = 3.

2. Write an equation in standard from of the line through (3,-1) and (2,-3)

Exampel 3: Write an equation of the specified line.

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a. Blue Line

b. Red Line

Exampel 4: Find the missing coefficient in the equation of the line shown. Write the completed equation.

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Guided Practice:a. Write the equations of the horizonatl and verticel lines that pass through the give point.

(-8,-9)

b. Find the missing coefficient in the equation of th eline that passes through the given point. Write the completed equation.

1. −4x + By = 7, (-1,10)

2. Ax + y = −3, (2,11)

Example 5: Your class is taking a trip to the public library. You can travel in small or 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.

a. Write an equation in standard form that models the possible combinations of small vans and large vans that your class can fill.

b. Graph the equation.

c. List Several Combinations.

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5. Ch 5.5: Write Equations of Parallel and Perpendicular Lines

Key Concept:

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•If two nonverticle lines in the same plane have the same slope, then they are parallel.

•If two nonverticle lines in the same plane are parallel, then they have the same slope.

Example 1: Write an equation of the line that passes through (-3,-5) and is parallel to the line y = 3x − 1.

Write an equation of the line that passes through (-2,11) and is parallel to the line y = −x + 5.

A. _____________________: two lines in the same plane that intersect to form a right angle.

Key Concept:

Perpendicular Lines

•If two nonvertical lines in the same plane have slopes that are negative reciprocals, then the lines are perpendicular.

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•If two nonvertical lines in the same plane are perpendicular, then their slopes are negative reciprocals.

Example 2: Determine which lines, if any, are parallel or perpendicular.

Line a: y = 5x − 3

Line b: x + 5y = 2

Line c: −10y − 2x = 0

Example 3: The Arizona state flag is shown in a coordinate plane. Lines a and b appear to be perpendicular. Are they

Line a: 12y = −7x + 42Line b: 11y = 16x − 52

Example 4: Write the equation of the line that passes through (4,-5) and is perpendicular to the line y = 2x + 3.

Write the equation of the line that passes through (4,3) and is perpendicular to the line y = 4x − 7.