Equations of Lines in Algebra

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Questions and Answers

The equation of a line can be found for which of the following situations? (Select all that apply)

  • A point on the line and the slope are known. (correct)
  • Two points on the line are known. (correct)

Indicate in standard form the equation of the line passing through the points A(4, 1) and B(5, 2).

x - y = 3

Indicate in standard form the equation of the line passing through the points R(3, 3) and S(-6, -6).

x - y = 0

Indicate in standard form the equation of the line passing through the points B(0, 0) and C(4, -4).

<p>x + y = 0</p> Signup and view all the answers

Indicate in standard form the equation of the line passing through the points P(6, 2) and Q(8, -4).

<p>3x + y = 20</p> Signup and view all the answers

Indicate in standard form the equation of the line passing through the points M(0, 6) and N(6, 0).

<p>x + y = 6</p> Signup and view all the answers

Indicate in standard form the equation of the line passing through the points E(-2, 2) and F(5, 1).

<p>x + 7y = 12</p> Signup and view all the answers

Indicate in standard form the equation of the line passing through the points G(4, 6) and H(1, 5).

<p>x - 3y = -14</p> Signup and view all the answers

Indicate in standard form the equation of the line passing through the points S(1/2, 1) and T(1/2, 4).

<p>x = 1/2</p> Signup and view all the answers

Indicate in standard form the equation of the line passing through the points L(5, 0) and M(0, 5).

<p>x + y = 5</p> Signup and view all the answers

Indicate in standard form the equation of the line passing through the points X(0, 6) and Y(5, 6).

<p>y = 6</p> Signup and view all the answers

Indicate in standard form the equation of the line passing through the point A(5, 5) with a slope m = 3.

<p>3x - y = 10</p> Signup and view all the answers

Indicate in standard form the equation of the line passing through the point B(6, 2) with a slope m = 1/2.

<p>x + 2y = 10</p> Signup and view all the answers

Indicate in standard form the equation of the line passing through the point C(0, 4) with a slope m = 0.

<p>y = 4</p> Signup and view all the answers

Indicate in standard form the equation of the line passing through the point D(5, -2) with a slope m = 2/5.

<p>2x - 5y = 20</p> Signup and view all the answers

Indicate in standard form the equation of the line passing through the point E(3, 5) with a slope m = undefined.

<p>x = 3</p> Signup and view all the answers

Indicate the equation of the line through (2, -1) and parallel to a line with slope of 3/4.

<p>3x - 4y = 10</p> Signup and view all the answers

Indicate the equation of the line through the point (-3, 4) and perpendicular to a line with a given slope.

<p>5x + 2y = -7</p> Signup and view all the answers

Indicate the equation of the line with slope and containing the midpoint of the segment with endpoints (2, -3) and (-6, 5).

<p>9x - 7y = -25</p> Signup and view all the answers

Indicate the equation of the line through the midpoint of and perpendicular to the segment joining (1, 0) and (5, -2).

<p>2x - y = 7</p> Signup and view all the answers

Indicate the equation of the line containing the midpoints of the legs of right triangle ABC with vertices A(-5, 5), B(1, 1), C(3, 4).

<p>x + 8y = 22</p> Signup and view all the answers

Indicate the equation of the line containing the hypotenuse of right triangle ABC with vertices A(-5, 5), B(1, 1), C(3, 4).

<p>x + 8y = 35</p> Signup and view all the answers

Indicate the equation of the line containing the longer diagonal of a quadrilateral with vertices A(2, 2), B(-2, -2), C(1, -1), D(6, 4).

<p>3x - 4y = 2</p> Signup and view all the answers

Indicate the equation of the line containing the median of the trapezoid with vertices R(-1, 5), S(1, 8), T(7, -2), U(2, 0).

<p>10x + 6y = 39</p> Signup and view all the answers

Indicate the equation of the line containing the altitude to the hypotenuse of a right triangle with vertices P(-1, 1), Q(3, 5), R(5, -5).

<p>x - 5y = -6</p> Signup and view all the answers

Indicate the equations of the diagonals of a square with vertices A(-3, 3), B(3, 3), C(3, -3), D(-3, -3).

<p>x +/- y = 0</p> Signup and view all the answers

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Study Notes

Situation of Lines

  • An equation of a line can be determined if either two points on the line are known or a point on the line and the slope are provided.

Standard Form Equations of Lines

  • Line through points A(4, 1) and B(5, 2): x - y = 3
  • Line through points R(3, 3) and S(-6, -6): x - y = 0
  • Line through points B(0, 0) and C(4, -4): x + y = 0
  • Line through points P(6, 2) and Q(8, -4): 3x + y = 20
  • Line through points M(0, 6) and N(6, 0): x + y = 6
  • Line through points E(-2, 2) and F(5, 1): x + 7y = 12
  • Line through points G(4, 6) and H(1, 5): x - 3y = -14
  • Line through points S(1/2, 1) and T(1/2, 4): x = 1/2
  • Line through points L(5, 0) and M(0, 5): x + y = 5
  • Line through points X(0, 6) and Y(5, 6): y = 6

Lines with Given Points and Slopes

  • Point A(5, 5) with slope m = 3: 3x - y = 10
  • Point B(6, 2) with slope m = 1/2: x + 2y = 10
  • Point C(0, 4) with slope m = 0: y = 4 (horizontal line)
  • Point D(5, -2) with slope m = 2/5: 2x - 5y = 20
  • Point E(3, 5) with slope m = undefined: x = 3 (vertical line)

Specific Line Requirements

  • Line through point (2, -1) parallel to slope 3/4: 3x - 4y = 10
  • Line through point (-3, 4) perpendicular to another slope: 5x + 2y = -7
  • Line with midpoint between points (2, -3) and (-6, 5): 9x - 7y = -25
  • Line through the midpoint, perpendicular to points (1, 0) and (5, -2): 2x - y = 7
  • Line through midpoints of triangle ABC (A(-5, 5), B(1, 1), C(3, 4)): x + 8y = 22
  • Line containing the hypotenuse of triangle ABC: x + 8y = 35
  • Line containing the longer diagonal of quadrilateral with vertices A(2, 2), B(-2, -2), C(1, -1), D(6, 4): 3x - 4y = 2
  • Line containing the median of trapezoid with vertices R(-1, 5), S(1, 8), T(7, -2), U(2, 0): 10x + 6y = 39
  • Line containing the altitude to the hypotenuse of triangle P(-1, 1), Q(3, 5), R(5, -5): x - 5y = -6
  • Equations for diagonals of square with vertices A(-3, 3), B(3, 3), C(3, -3), D(-3, -3): x +/- y = 0 (representing both diagonals)

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