Algebra Chapter 4
Writing Linear Equations
4.1 Write Linear Equations in Slope-Intercept Form
y-intercept: ______
Slope: ______
Slope-intercept form: ______
Example 1: Write an equation of the line with a slope of and a y-intercept of –7.
Example 2: Write an equation of the line shown.
Example 3: Write an equation for the linear function f with the values f (0) = 7 and f (12) = 15.
Example 4: A dance academy charges $20 to use the facility and $25 per hour of instruction.
- Write and equation that gives the total cost to learn dance at the academy as a function of hours of instruction.
- Find the total cost of 2 hours of dance instruction.
4.2 Use Linear Equations in Slope-Intercept Form
Example 1: Write an equation of the line that passes through the point (2, 5) and has a slope of 3.
Example 2: Write an equation of the line that passes through (3, 9) and (22, 21).
Example 3: Write an equation of the linear function with the values f (2) = 3 and f (–3) = 8.
Example 4: A carnival charges $2.50 per ride after an entrance fee. You paid a total of $22.50 after 6 rides. Write an equation that gives the total cost as a function of the number of rides. Find the cost for 15 rides.
4.3 Write Linear Equations in Point-Slope Form
Point-slope form: ______
Example 1: Write an equation in point-slope form of the line that passes through the point (5, 1) and has a slope of –3.
Example 2: Graph the equation y – 2 = – (x + 4).
Example 3: Write an equation in point-slope form of the line shown.
Example 4: A radio station charges $650 for the first minute of ad time and then $340 for each additional minute. Write an equation that gives the total cost (in dollars) to run an ad as a function of the number of minutes the ad runs. Find the cost of 7 minutes of ad time.
4.4 Write Linear Equations in Standard Form
Standard Form: ______
Example 1: Write two equations in standard form that are equivalent to 3x – 9y = 12.
Example 2: Write an equation in standard form of the line shown.
Example 3: Write equations of the horizontal and vertical lines that pass through the point (–2, 8).
Example 4: The graph of 5x + By = 6 is a line that passes through the point (2, 1).
Find the missing coefficient and write the completed equation.
Example 5: T-shirts at a flea market cost $4.50 each and shorts cost $6 each. You have enough money to buy exactly 12 t-shirts and 9 pairs of shorts.
- Write an equation in standard form that models the possible combinations of t-shirts and shorts you can buy.
- Graph the equation.
- List several possible combinations.
4.5 Write Equations of Parallel and Perpendicular Lines
Converse: ______
Perpendicular Lines: ______
Properties of Parallel lines:
______
______
Properties of Perpendicular Lines:
______
Example 1: Write an equation of the line that passes through (2, 6) and is parallel to the line
y = –x+ 2.
Example 2: Determine which of the following lines, if any, are parallel or perpendicular:
Line a: 4y – 6x = –8, Line b: y = x + 1, Line c: 2x + 3y = –15.
Example 3: Write an equation of the line that passes through (–2, 1) and is perpendicular to the line
y = x + 2.
4.6 Fit a Line to Data
Scatter plot: ______
Positive Correlation: ______
Negative Correlation: ______
Relatively no correlation: ______
Line of Fit: ______
Example 1: Describe the correlation of data graphed in the scatter plot. The data on the graph shows the result of a forest ranger’s annual survey on rabbit and red-tail hawk population.
a.
Example 2:The table shows the number of girls signed up for a summer softball league each year for 5 years.
a.Make a scatter plot of the data.
b.Describe the correlation of the data.
c.Write an equation that models the number of girls signed up for a summer softball league as a function of the number of years since 2000.
Year / 2001 / 2002 / 2003 / 2004 / 2005Players / 105 / 113 / 120 / 132 / 148
/
4.7 Predict With Linear Models
Best-fitting line: ______
Linear Regression: ______
Interpolation: ______
Extrapolation: ______
Zero of a function: ______
Example 1: The table shows the number of pairs of nesting Bald Eagles at a national wildlife reserve from 1998 to 2002.
Year / 1998 / 2000 / 2001 / 2002Pairs of Nesting Eagles / 5 / 12 / 18 / 25
a.Make a scatter plot of the data.
b.Find an equation that models the number of pairs of nesting Bald Eagles as a function of the number of years since 1998.
c.Approximate the number of nesting eagle pairs in 1999.
Example 2: Look back at Example 1.
a.Use the equation from Example 1 to approximate the number of nesting Bald Eagle pairs in 2003 and 2005.
b.In 2003 there were actually 31 pairs of nesting eagles. In 2005 there were actually 34 pairs of nesting eagles. Describe the accuracy of the extrapolations made in part (a).
Example 3: Find the zeros of the following functions.