Honors Algebra 2: Extra Practice on Linear Equations Worksheet 1

  1. Given \(y = 4x + 2\)
    1. Find the line's x-intercept(s)
      2. Solution \( \displaystyle \left( -\frac{1}{2}, 0 \right) \)
    2. Find the line's y-intercept(s)
      3. Solution (0, 2)
    3. Find the line's slope.
      4. Solution 4
    4. Write the equation of the line in standard form.
      5. Solution \(4x - y = -2\)
  2. Given \( \displaystyle y - 6 = \frac{3}{4}(x + 1)\)
    1. Find the line's x-intercept(s)
      2. Solution (-9, 0)
    2. Find the line's y-intercept(s)
      3. Solution \( \displaystyle (0, \frac{27}{4}) \)
    3. Find the line's slope.
      4. Solution \( \displaystyle \frac{3}{4}\)
    4. Write the equation of the line in standard form.
      5. Solution \(3x - 4y -27\)
  3. Given \( \displaystyle -\frac{x}{8} + \frac{2y}{3} = 1 \)
    1. Find the line's x-intercept(s)
      2. Solution (-8, 0)
    2. Find the line's y-intercept(s)
      3. Solution \( \displaystyle \left( 0, \frac{3}{2}\right) \)
    3. Find the line's slope.
      4. Solution \( \displaystyle \frac{3}{16}\)
    4. Write the equation of the line in standard form.
      5. Solution \( 3x - 16y = -24\)
  4. Given \( 3(2x - 7) = 6x + 9y \)
    1. Find the line's x-intercept(s)
      2. Solution There is no x-intercept
    2. Find the line's y-intercept(s)
      3. Solution \( \displaystyle \left( 0, -\frac{7}{3} \right) \)
    3. Find the line's slope.
      4. Solution 0
    4. Write the equation of the line in standard form.
      5. Solution \( 0x + 3y = -7\)
  5. Given \( -9x + 6y = -2 \)
    1. Find the line's x-intercept(s)
      2. Solution \( \displaystyle \left( \frac{9}{2}, 0 \right) \)
    2. Find the line's y-intercept(s)
      3. Solution \( \displaystyle \left( 0, -\frac{1}{3} \right) \)
    3. Find the line's slope.
      4. Solution \( \displaystyle \frac{3}{2} \)
    4. Write the equation of the line in standard form.
      5. Solution \( 9x - 6y = 2 \)
  6. Find the equation of the line through the points (8, -1) and (3, -2). Answer in standard form.
    7. Solution \( \displaystyle y + 1 = \frac{1}{5} \left( x - 8 \right) \); In standard form, that's \(x - 5y = 13\).
  7. Find the equation of the line parallel to the line 5x + 8y = 7 that goes through the point (4, 0). Answer in standard form.

    8. Solution \( \displaystyle y - 0= -\frac{5}{8}\left(x - 4 \right) \); In standard form, that's \(5x + 8y = 20\).

  8. Find the equation of the perpendicular bisector of the segment through the points (5, 1) and (-2, 13). Answer in standard form.
    9. Solution \( \displaystyle y - 7 = \frac{7}{12} \left( x - \frac{3}{2} \right) \); In standard form, that's \(14x - 24y = -147\).
  9. Find the equation of the line through (12, 21) perpendicular to the line y = 3. Answer in standard form.
    10. Solution \( x = 12\). In standard form, that's \(x + 0y = 12\)
  10. Find the equation of the line parallel to the y-axis that goes through the point (4, -1). Answer in standard form.
    11. Solution \( x = 4\). In standard form, that's \(x + 0y = 4\)
  11. Find the equation of the line with y-intercept (0, 9) with no x-intercept. Answer in standard form.
    12. Solution \( y = 9\). In standard form, that's \(0x + y = 9\)
  12. Find the equation of the line with slope 3 and x-intercept 4. Leave your answer in the easiest form.
    13. Solution \( y - 0 = 3(x - 4)\)
  13. Find the equation of the line with y-intercept \( \displaystyle -\frac{3}{2}\) and the same slope as \( \displaystyle \frac{x}{2} = -2y + 1\). Leave your answer in the easiest form.
    14. Solution \( \displaystyle y = -\frac{1}{4}x - \frac{3}{2}\)
  14. Find the equation of the line with slope 0 through (-2, 6). Leave your answer in the easiest form.
    15. Solution \( y = 6 \)
  15. Find the equation of the line through (4, 9) with the same slope as x = 10. Leave your answer in the easiest form.
    16. Solution \( x = 4 \)
  16. Find the equation of the line through (3, -1) and parallel to 4x - 3y = 16. Leave your answer in the easiest form.
    17. Solution \( \displaystyle y + 1 = \frac{4}{3}(x - 3)\)
  17. Find the value of \(a\) for which the line through points P\( \displaystyle \left( 4, \frac{1}{a + 1} \right)\) and Q(10, 3) have the same slope as the line \(-4x + y = 18\).
    18. Solution \( \displaystyle 4 = \frac{3 - \frac{1}{a + 1}}{10 - 4} = \frac{3 - \frac{1}{a + 1}}{6}\). Multiply both sides of the equation by 6 to get: \( \displaystyle 24 = 3 - \frac{1}{a + 1}\) (and \(a \neq -1\)). Multiply both sides by \(a + 1\) to get \(24(a + 1) = 3(a + 1) - 1\), so \(21(a + 1) = -1\), or \(21a + 21 = -1\), and \( \displaystyle a = -\frac{22}{21}\).