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given 2 points find the slope using the slope formula. show all work. $…

\( \frac{7}{6} \) ### Problem 2: (-5, 3) and (-1, 0)

カテゴリ: algebra 更新日: 2026-02-04

問題

given 2 points find the slope using the slope formula. show all work.
$m=\\frac{y_2 - y_1}{x_2 - x_1}$

  1. ( 1,2) and (7, 9) 2. (-5, 3) and (-1,0)
  2. (5,-1) and (0, 3) 4. (6,2) and (6,-5)
  3. (12,5) and ( 9,8) 6. (-3,-7) and (-8, -1)
  4. (2,-5) and (7,-5) 8. ( 2, ¾ ) and ( 4, ¼ )
  5. ( ½, 2/3 ) and (0, 1/3) 10. (3,-5) and (0,0)

解法ステップ

  1. Understand the question

    given 2 points find the slope using the slope formula. show all work.
    $m=\\frac{y_2 - y_1}{x_2 - x_1}$

    1. ( 1,2) and (7, 9) 2. (-5, 3) and (-1,0)
    2. (5,-1) and (0, 3) 4. (6,2) and (6,-5)
    3. (12,5) and ( 9,8) 6. (-3,-7) and (-8, -1)
    4. (2,-5) and (7,-5) 8. ( 2, ¾ ) and ( 4, ¼ )
    5. ( ½, 2/3 ) and (0, 1/3) 10. (3,-5) and (0,0)
  2. Response
    Problem 1: (1, 2) and (7, 9)
  3. Explanation

    Step 1: Identify \( x_1, y_1, x_2, y_2 \)

    Let \( (x_1, y_1) = (1, 2) \) and \( (x_2, y_2) = (7, 9) \).

    Step 2: Apply slope formula

    \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{9 - 2}{7 - 1} = \frac{7}{6} \)

  4. Explanation

    Step 1: Identify \( x_1, y_1, x_2, y_2 \)

    Let \( (x_1, y_1) = (-5, 3) \) and \( (x_2, y_2) = (-1, 0) \).

    Step 2: Apply slope formula

    \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 3}{-1 - (-5)} = \frac{-3}{4} = -\frac{3}{4} \)

  5. Explanation

    Step 1: Identify \( x_1, y_1, x_2, y_2 \)

    Let \( (x_1, y_1) = (5, -1) \) and \( (x_2, y_2) = (0, 3) \).

    Step 2: Apply slope formula

    \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - (-1)}{0 - 5} = \frac{4}{-5} = -\frac{4}{5} \)

  6. Final answer

    \( \frac{7}{6} \)

    Problem 2: (-5, 3) and (-1, 0)

答え

Response

Problem 1: (1, 2) and (7, 9)

Explanation

Step 1: Identify \( x_1, y_1, x_2, y_2 \)

Let \( (x_1, y_1) = (1, 2) \) and \( (x_2, y_2) = (7, 9) \).

Step 2: Apply slope formula

\( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{9 - 2}{7 - 1} = \frac{7}{6} \)

Answer

\( \frac{7}{6} \)

Problem 2: (-5, 3) and (-1, 0)

Explanation

Step 1: Identify \( x_1, y_1, x_2, y_2 \)

Let \( (x_1, y_1) = (-5, 3) \) and \( (x_2, y_2) = (-1, 0) \).

Step 2: Apply slope formula

\( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 3}{-1 - (-5)} = \frac{-3}{4} = -\frac{3}{4} \)

Answer

\( -\frac{3}{4} \)

Problem 3: (5, -1) and (0, 3)

Explanation

Step 1: Identify \( x_1, y_1, x_2, y_2 \)

Let \( (x_1, y_1) = (5, -1) \) and \( (x_2, y_2) = (0, 3) \).

Step 2: Apply slope formula

\( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - (-1)}{0 - 5} = \frac{4}{-5} = -\frac{4}{5} \)

Answer

\( -\frac{4}{5} \)

Problem 4: (6, 2) and (6, -5)

Explanation

Step 1: Identify \( x_1, y_1, x_2, y_2 \)

Let \( (x_1, y_1) = (6, 2) \) and \( (x_2, y_2) = (6, -5) \).

Step 2: Apply slope formula

\( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - 2}{6 - 6} = \frac{-7}{0} \) (undefined, vertical line)

Answer

Undefined

Problem 5: (12, 5) and (9, 8)

Explanation

Step 1: Identify \( x_1, y_1, x_2, y_2 \)

Let \( (x_1, y_1) = (12, 5) \) and \( (x_2, y_2) = (9, 8) \).

Step 2: Apply slope formula

\( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 5}{9 - 12} = \frac{3}{-3} = -1 \)

Answer

\( -1 \)

Problem 6: (-3, -7) and (-8, -1)

Explanation

Step 1: Identify \( x_1, y_1, x_2, y_2 \)

Let \( (x_1, y_1) = (-3, -7) \) and \( (x_2, y_2) = (-8, -1) \).

Step 2: Apply slope formula

\( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - (-7)}{-8 - (-3)} = \frac{6}{-5} = -\frac{6}{5} \)

Answer

\( -\frac{6}{5} \)

Problem 7: (2, -5) and (7, -5)

Explanation

Step 1: Identify \( x_1, y_1, x_2, y_2 \)

Let \( (x_1, y_1) = (2, -5) \) and \( (x_2, y_2) = (7, -5) \).

Step 2: Apply slope formula

\( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - (-5)}{7 - 2} = \frac{0}{5} = 0 \) (horizontal line)

Answer

\( 0 \)

Problem 8: (2, \( \frac{3}{4} \)) and (4, \( \frac{1}{4} \))

Explanation

Step 1: Identify \( x_1, y_1, x_2, y_2 \)

Let \( (x_1, y_1) = (2, \frac{3}{4}) \) and \( (x_2, y_2) = (4, \frac{1}{4}) \).

Step 2: Apply slope formula

\( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\frac{1}{4} - \frac{3}{4}}{4 - 2} = \frac{-\frac{2}{4}}{2} = \frac{-\frac{1}{2}}{2} = -\frac{1}{4} \)

Answer

\( -\frac{1}{4} \)

Problem 9: (\( \frac{1}{2} \), \( \frac{2}{3} \)) and (0, \( \frac{1}{3} \))

Explanation

Step 1: Identify \( x_1, y_1, x_2, y_2 \)

Let \( (x_1, y_1) = (\frac{1}{2}, \frac{2}{3}) \) and \( (x_2, y_2) = (0, \frac{1}{3}) \).

Step 2: Apply slope formula

\( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\frac{1}{3} - \frac{2}{3}}{0 - \frac{1}{2}} = \frac{-\frac{1}{3}}{-\frac{1}{2}} = \frac{2}{3} \)

Answer

\( \frac{2}{3} \)

Problem 10: (3, -5) and (0, 0)

Explanation

Step 1: Identify \( x_1, y_1, x_2, y_2 \)

Let \( (x_1, y_1) = (3, -5) \) and \( (x_2, y_2) = (0, 0) \).

Step 2: Apply slope formula

\( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-5)}{0 - 3} = \frac{5}{-3} = -\frac{5}{3} \)

Answer

\( -\frac{5}{3} \)

Question Image

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Question Analysis

Subject unspecified
Sub Subject unspecified
Education Level not specified
Difficulty unspecified
Question Type calculation
Multi Question No
Question Count 1
Analysis Status completed
Analyzed At 2026-02-04T16:40:35

OCR Text

Show OCR extraction 
given 2 points find the slope using the slope formula. show all work.
$m=\\frac{y_2 - y_1}{x_2 - x_1}$
1. ( 1,2) and (7, 9)  2. (-5, 3) and (-1,0)
3. (5,-1) and (0, 3)  4. (6,2) and (6,-5)
5. (12,5) and ( 9,8)  6. (-3,-7) and (-8, -1)
7. (2,-5) and (7,-5)  8. ( 2, ¾ ) and ( 4, ¼ )
9. ( ½, 2/3 ) and (0, 1/3)  10. (3,-5) and (0,0)

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