Point Slope Word Problems

A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet.

What is the average rate of change?

What is a point-slope equation for the climber?

• 200 ; y - 700 = 200(x - 6)

• 75 ; y - 6 = 75(x - 700)

• 300 ; y - 700 = 300(x - 6)

• 75 ; y - 700 = 75(x - 6)

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At 0 seconds, Mrs. Taylor was 10 feet off the ground. At 5 seconds, she was 20 feet off the ground. Write two point-slope form equations for the problem.

• y - 0 = 2(x - 10)

  y - 5 = 2(x - 20)

• y - 0 = 5(x - 10)

  y - 5 = 5(x- 20)

• y - 10 = 2(x - 0)

  y - 20 = 2(x -5)

• y - 10 = 6(x - 0)

  y - 20 = 6(x - 5)

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11. Which of the following is NOT true about the graph of the line
y + 4 = -5(x - 1)

• It goes through the point (-4, 1)
• It has a slope of -5
• The equation is in point-slope form
• It goes through the point (4, -1)

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CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

Violet has an Internet business selling paint sets.  After an initial website fee each week, she makes a profit of $0.75 on each set she sells.  If she sells 8 sets and she makes $2.25; write an equation in point-slope form representing her weekly possible earnings.

• y - 2.25 = 0.75(x - 8)
• y - 8 = 0.75(x - 2.25)
• y - 8 = 2.25(x - 0.75)
• y - 0.75 = 2.25(x - 8)

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A sign says that 3 tickets cost $22.50 and that 7 tickets cost $52.50. Which equations in point-slope form would represents the cost of tickets? Select all that apply.

• y - 22.50 = 7.50(x - 3)

• y - 52.50 = 7.50(x - 7)

• y = 7.50x

• y + 22.50 = 7.50(x + 3)

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CCSS.HSA.CED.A.2

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To order tickets online to a hockey game, there is a processing fee plus the cost per ticket. The cost for 5 tickets is $102.00 The cost for 8 tickets is $150. What are the two points that we could use to find a linear equation for cost, C, of t tickets?

•  $\left(5,8\right)\ \&\ \left(102,\ 150\right)$ 

•  $\left(8,5\right)\ \&\ \left(150,102\right)$ 

•  $\left(5,102\right)\ \&\ \left(8,150\right)$ 

•  $\left(102,5\right)\ \&\ \left(150,8\right)$ 

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CCSS.HSA.CED.A.2

Find the rate of change.

Then write the point-slope equation.

• -2 minutes per gallon

  y - 80 = -2 (x - 10)

• -20 minutes per gallon

  y - 80 = -20 (x - 10)

• -2 gallons per minute

  y -80 = -2 (x - 10)

• -20 gallons per minute

  y - 80 = -20 (x - 10)

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CCSS.HSA.CED.A.2

CCSS.HSS.ID.C.7

For the equation
y - 3 = 2(x + 4),
the line has a slope of 2 and contains what point?

• (-4, 3)
• (3, -4)
• (-3, -4)
• (-4, -3)

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CCSS.HSA.CED.A.2

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Which of these represents point-slope form of a linear equation?

• y - y₁ = m(x - x₁)
• Ax + By = C
• y = mx + b

For the equation 
y - 4 = -1/3(x - 7), 
what are the coordinates for the point?

• (4, 7)
• (-7, - 4)
• (7, 4)
• (-4, -7)

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CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

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