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Lesson Menu Five-Minute Check (over Lesson 3–3) CCSS Then/Now New Vocabulary Key Concept: Nonvertical Line Equations Example 1:Slope and y-intercept Example 2:Slope and a Point on the Line Example 3:Two Points Example 4:Horizontal Line Key Concept: Horizontal and Vertical Line Equations Example 5:Write Equations of Parallel or Perpendicular Lines Example 6:Real-World Example: Write Linear Equations

Over Lesson 3–3 5-Minute Check 1 A. B. C. D. What is the slope of the line MN for M(–3, 4) and N(5, –8)?

Over Lesson 3–3 5-Minute Check 1 A. B. C. D. What is the slope of the line MN for M(–3, 4) and N(5, –8)?

Over Lesson 3–3 5-Minute Check 2 A. B. C. D. What is the slope of a line perpendicular to MN for M(–3, 4) and N(5, –8)?

Over Lesson 3–3 5-Minute Check 2 A. B. C. D. What is the slope of a line perpendicular to MN for M(–3, 4) and N(5, –8)?

Over Lesson 3–3 5-Minute Check 3 A. B. C. D. What is the slope of a line parallel to MN for M(–3, 4) and N(5, –8)?

Over Lesson 3–3 5-Minute Check 3 A. B. C. D. What is the slope of a line parallel to MN for M(–3, 4) and N(5, –8)?

Over Lesson 3–3 A.B. C.D. 5-Minute Check 4 What is the graph of the line that has slope 4 and contains the point (1, 2)?

Over Lesson 3–3 A.B. C.D. 5-Minute Check 4 What is the graph of the line that has slope 4 and contains the point (1, 2)?

Over Lesson 3–3 5-Minute Check 5 What is the graph of the line that has slope 0 and contains the point (–3, –4)? A.B. C.D.

Over Lesson 3–3 5-Minute Check 5 What is the graph of the line that has slope 0 and contains the point (–3, –4)? A.B. C.D.

Over Lesson 3–3 5-Minute Check 6 A.(–2, 2) B.(–1, 3) C.(3, 3) D.(4, 2)

Over Lesson 3–3 5-Minute Check 6 A.(–2, 2) B.(–1, 3) C.(3, 3) D.(4, 2)

CCSS Content Standards G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Mathematical Practices 4 Model with mathematics. 8 Look for and express regularity in repeated reasoning.

Then/Now You found the slopes of lines. Write an equation of a line given information about the graph. Solve problems by writing equations.

Vocabulary slope-intercept form point-slope form

Concept

Example 1 Slope and y-intercept Write an equation in slope-intercept form of the line with slope of 6 and y-intercept of –3. Then graph the line. y = mx + bSlope-intercept form y = 6x + (–3)m = 6, b = –3 y = 6x – 3 Simplify.

Example 1 Slope and y-intercept Answer: Plot a point at the y-intercept, –3. Use the slope of 6 or to find another point 6 units up and 1 unit right of the y-intercept. Draw a line through these two points.

Example 1 Slope and y-intercept Answer: Plot a point at the y-intercept, –3. Use the slope of 6 or to find another point 6 units up and 1 unit right of the y-intercept. Draw a line through these two points.

Example 1 A.x + y = 4 B.y = x – 4 C.y = –x – 4 D.y = –x + 4 Write an equation in slope-intercept form of the line with slope of –1 and y-intercept of 4.

Example 1 A.x + y = 4 B.y = x – 4 C.y = –x – 4 D.y = –x + 4 Write an equation in slope-intercept form of the line with slope of –1 and y-intercept of 4.

Example 2 Slope and a Point on the Line Point-slope form Write an equation in point-slope form of the line whose slope is that contains (–10, 8). Then graph the line. Simplify.

Example 2 Slope and a Point on the Line Answer: Graph the given point (–10, 8). Use the slope to find another point 3 units down and 5 units to the right. Draw a line through these two points.

Example 2 Slope and a Point on the Line Answer: Graph the given point (–10, 8). Use the slope to find another point 3 units down and 5 units to the right. Draw a line through these two points.

Example 2 Write an equation in point-slope form of the line whose slope is that contains (6, –3). A. B. C. D.

Example 2 Write an equation in point-slope form of the line whose slope is that contains (6, –3). A. B. C. D.

Example 3 Two Points A. Write an equation in slope-intercept form for a line containing (4, 9) and (–2, 0). Step 1 First, find the slope of the line. Slope formula x 1 = 4, x 2 = –2, y 1 = 9, y 2 = 0 Simplify.

Example 3 Two Points Step 2 Now use the point-slope form and either point to write an equation. Distributive Property Add 9 to each side. Answer: Point-slope form Using (4, 9):

Example 3 Two Points Step 2 Now use the point-slope form and either point to write an equation. Distributive Property Add 9 to each side. Answer: Point-slope form Using (4, 9):

Example 3 Two Points B. Write an equation in slope-intercept form for a line containing (–3, –7) and (–1, 3). Step 1 First, find the slope of the line. Slope formula x 1 = –3, x 2 = –1, y 1 = –7, y 2 = 3 Simplify.

Example 3 Two Points Step 2 Now use the point-slope form and either point to write an equation. Distributive Property Answer: m = 5, (x 1, y 1 ) = (–1, 3) Point-slope form Using (–1, 3): Add 3 to each side. y = 5x + 8

Example 3 Two Points Step 2 Now use the point-slope form and either point to write an equation. Distributive Property Answer: m = 5, (x 1, y 1 ) = (–1, 3) Point-slope form Using (–1, 3): Add 3 to each side. y = 5x + 8

Example 3a A. Write an equation in slope-intercept form for a line containing (3, 2) and (6, 8). A. B. C. D.

Example 3a A. Write an equation in slope-intercept form for a line containing (3, 2) and (6, 8). A. B. C. D.

Example 3b A.y = 2x – 3 B.y = 2x + 1 C.y = 3x – 2 D.y = 3x + 1 B. Write an equation in slope-intercept form for a line containing (1, 1) and (4, 10).

Example 3b A.y = 2x – 3 B.y = 2x + 1 C.y = 3x – 2 D.y = 3x + 1 B. Write an equation in slope-intercept form for a line containing (1, 1) and (4, 10).

Example 4 Horizontal Line Write an equation of the line through (5, –2) and (0, –2) in slope-intercept form. Slope formula This is a horizontal line. Step 1

Example 4 Horizontal Line Point-Slope form m = 0, (x 1, y 1 ) = (5, –2) Step 2 Answer: Simplify. Subtract 2 from each side.y = –2

Example 4 Horizontal Line Point-Slope form m = 0, (x 1, y 1 ) = (5, –2) Step 2 Answer: Simplify. Subtract 2 from each side.y = –2

Example 4 Write an equation of the line through (–3, 6) and (9, –2) in slope-intercept form. A. B. C. D.

Example 4 Write an equation of the line through (–3, 6) and (9, –2) in slope-intercept form. A. B. C. D.

Concept

Example 5 Write Equations of Parallel or Perpendicular Lines y =mx + bSlope-Intercept form 0 =–5(2) + bm = –5, (x, y) = (2, 0) 0 =–10 + bSimplify. 10 =bAdd 10 to each side. Answer:

Example 5 Write Equations of Parallel or Perpendicular Lines y =mx + bSlope-Intercept form 0 =–5(2) + bm = –5, (x, y) = (2, 0) 0 =–10 + bSimplify. 10 =bAdd 10 to each side. Answer: So, the equation is y = –5x + 10.

A.y = 3x B.y = 3x + 8 C.y = –3x + 8 D. Example 5

A.y = 3x B.y = 3x + 8 C.y = –3x + 8 D. Example 5

Example 6 Write Linear Equations RENTAL COSTS An apartment complex charges $525 per month plus a $750 annual maintenance fee. A. Write an equation to represent the total first year’s cost A for r months of rent. For each month of rent, the cost increases by $525. So the rate of change, or slope, is 525. The y-intercept is located where 0 months are rented, or $750. A= mr + bSlope-intercept form A= 525r + 750m = 525, b = 750 Answer:

Example 6 Write Linear Equations RENTAL COSTS An apartment complex charges $525 per month plus a $750 annual maintenance fee. A. Write an equation to represent the total first year’s cost A for r months of rent. For each month of rent, the cost increases by $525. So the rate of change, or slope, is 525. The y-intercept is located where 0 months are rented, or $750. A= mr + bSlope-intercept form A= 525r + 750m = 525, b = 750 Answer: The total annual cost can be represented by the equation A = 525r

Example 6 Write Linear Equations RENTAL COSTS An apartment complex charges $525 per month plus a $750 annual maintenance fee. Evaluate each equation for r = 12. First complex:Second complex: A= 525r + 750A= 600r = 525(12) + 750r = 12= 600(12) = 7050Simplify.= 7400 B. Compare this rental cost to a complex which charges a $200 annual maintenance fee but $600 per month for rent. If a person expects to stay in an apartment for one year, which complex offers the better rate?

Example 6 Write Linear Equations Answer:

Example 6 Write Linear Equations Answer: The first complex offers the better rate: one year costs $7050 instead of $7400.

Example 6a A.C = 25 + d B.C = 125d C.C = 100d + 25 D.C = 25d RENTAL COSTS A car rental company charges $25 per day plus a $100 deposit. A. Write an equation to represent the total cost C for d days of use.

Example 6a A.C = 25 + d B.C = 125d C.C = 100d + 25 D.C = 25d RENTAL COSTS A car rental company charges $25 per day plus a $100 deposit. A. Write an equation to represent the total cost C for d days of use.

Example 6b A.first company B.second company C.neither D.cannot be determined RENTAL COSTS A car rental company charges $25 per day plus a $100 deposit. B. Compare this rental cost to a company which charges a $50 deposit but $35 per day for use. If a person expects to rent a car for 9 days, which company offers the better rate?

Example 6b A.first company B.second company C.neither D.cannot be determined RENTAL COSTS A car rental company charges $25 per day plus a $100 deposit. B. Compare this rental cost to a company which charges a $50 deposit but $35 per day for use. If a person expects to rent a car for 9 days, which company offers the better rate?

End of the Lesson