Lesson 9

Equations of Lines

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Problem 1

Select all the equations that represent the graph shown.

graph of line with points 0 comma -4, 2 comma 0 and 4 comma 3 plotted on line.
A:

\(3x-2y=6\)

B:

\(y=\frac{3}{2}x+3\)

C:

\(y=\frac{3}{2}x-3\)

D:

\(y-3=\frac{3}{2}(x-4)\)

E:

\(y-6=\frac{3}{2}(x-2)\)

Solution

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Problem 2

A line with slope \(\frac32\) passes through the point \((1,3)\).

  1. Explain why \((3,6)\) is on this line.
  2. Explain why \((0,0)\) is not on this line. 
  3. Is the point \((13,22)\) on this line? Explain why or why not.

Solution

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Problem 3

Write an equation of the line that passes through \((1,3)\) and has a slope of \(\frac{5}{4}\).

Solution

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Problem 4

A parabola has focus \((3,\text{-}2)\) and directrix \(y=2\). The point \((a,\text{-}8)\) is on the parabola. How far is this point from the focus?

A:

6 units

B:

8 units

C:

10 units

D:

cannot be determined

Solution

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(From Unit 6, Lesson 8.)

Problem 5

Write an equation for a parabola with each given focus and directrix.

  1. focus: \((5, 2)\); directrix: \(x\)-axis
  2. focus: \((\text{-}2, 3)\); directrix: the line \(y=7\)
  3. focus: \((0,7)\); directrix: \(x\)-axis
  4. focus: \((\text{-}3, \text- 4)\); directrix: the line \(y=\text-1\)

Solution

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(From Unit 6, Lesson 8.)

Problem 6

A parabola has focus \((\text{-}1,6)\) and directrix \(y=4\). Determine whether each point on the list is on this parabola. Explain your reasoning.

  1. \((\text{-}1,5)\)
  2. \((1 ,7)\)
  3. \((3, 9)\)

Solution

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(From Unit 6, Lesson 7.)

Problem 7

Select the center of the circle represented by the equation \(x^2 + y^2 - 8x + 11y - 2 = 0\).

A:

\((8, 11)\)

B:

\((4, 5.5)\)

C:

\((\text-4, \text-5.5)\)

D:

\((4, \text-5.5)\)

Solution

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(From Unit 6, Lesson 6.)

Problem 8

Reflect triangle \(ABC\) over the line \(x=\text-6\).

Translate the image by the directed line segment from \((0,0)\) to \((5,\text-1)\).

What are the coordinates of the vertices in the final image?

triangle ABC graphed. A = -5 comma 2, B = -6 comma -1, C = -3 comma 0.

Solution

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(From Unit 6, Lesson 1.)