Ask a New Question
Menu

Are the pairs of lines parallel, perpendicular, or intersecting?(3 points)

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
y−6=14(x+2)

y=−4x−10

2x−y=7

3x−4y=−8

y=−23x+7

−2x−3y=12
answers
parellel, perpendiculer, intersecting

1 answer

Let's analyze the given lines to determine if they are parallel, perpendicular, or intersecting.

  1. Line 1: \( y - 6 = 14(x + 2) \)

    • Rearranging to slope-intercept form (y = mx + b): \[ y - 6 = 14x + 28 \implies y = 14x + 34 \]
    • Slope (m) = 14

  2. Line 2: \( y = -4x - 10 \)

    • Slope (m) = -4

  3. Line 3: \( 2x - y = 7 \)

    • Rearranging to slope-intercept form: \[ -y = -2x + 7 \implies y = 2x - 7 \]
    • Slope (m) = 2

  4. Line 4: \( 3x - 4y = -8 \)

    • Rearranging to slope-intercept form: \[ -4y = -3x - 8 \implies y = \frac{3}{4}x + 2 \]
    • Slope (m) = \(\frac{3}{4}\)

  5. Line 5: \( y = -23x + 7 \)

    • Slope (m) = -23

  6. Line 6: \( -2x - 3y = 12 \)

    • Rearranging to slope-intercept form: \[ -3y = 2x + 12 \implies y = -\frac{2}{3}x - 4 \]
    • Slope (m) = -\(\frac{2}{3}\)

Now, let's compare the slopes to determine relationships:

  • Line 1 (Slope 14) and Line 2 (Slope -4): Not equal and not negative reciprocals, so they are intersecting.

  • Line 1 (Slope 14) and Line 3 (Slope 2): Not equal and not negative reciprocals, so they are intersecting.

  • Line 1 (Slope 14) and Line 4 (Slope 3/4): Not equal and not negative reciprocals, so they are intersecting.

  • Line 1 (Slope 14) and Line 5 (Slope -23): Not equal and not negative reciprocals, so they are intersecting.

  • Line 1 (Slope 14) and Line 6 (Slope -2/3): Not equal and not negative reciprocals, so they are intersecting.

  • Line 2 (Slope -4) and Line 3 (Slope 2): Not equal and not negative reciprocals, so they are intersecting.

  • Line 2 (Slope -4) and Line 4 (Slope 3/4): Not equal and not negative reciprocals, so they are intersecting.

  • Line 2 (Slope -4) and Line 5 (Slope -23): Not equal and not negative reciprocals, so they are intersecting.

  • Line 2 (Slope -4) and Line 6 (Slope -2/3): Not equal and not negative reciprocals, so they are intersecting.

  • Line 3 (Slope 2) and Line 4 (Slope 3/4): Not equal and not negative reciprocals, so they are intersecting.

  • Line 3 (Slope 2) and Line 5 (Slope -23): Not equal and not negative reciprocals, so they are intersecting.

  • Line 3 (Slope 2) and Line 6 (Slope -2/3): Not equal and not negative reciprocals, so they are intersecting.

  • Line 4 (Slope 3/4) and Line 5 (Slope -23): Not equal and not negative reciprocals, so they are intersecting.

  • Line 4 (Slope 3/4) and Line 6 (Slope -2/3): Not equal and not negative reciprocals, so they are intersecting.

  • Line 5 (Slope -23) and Line 6 (Slope -2/3): Not equal and not negative reciprocals, so they are intersecting.

In conclusion, all pairs of lines are intersecting. You can select "intersecting" for all pairs.