Question

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 y=−23x+7 −2x−3y=12 2x−y=7 3x−4y=−8

Answer 1

To determine the relationships between the pairs of lines (whether they are parallel, perpendicular, or intersecting), we need to analyze their slopes.

1. First Equation: y − 6 = 14(x + 2)

   • Rearranging this to slope-intercept form (y = mx + b):
   • y = 14x + 28 + 6
   • y = 14x + 34
   • Slope = 14

2. Second Equation: y = −4x − 10

   • Slope = -4

3. Third Equation: y = −23x + 7

   • Slope = -23

4. Fourth Equation: -2x - 3y = 12

   • Rearranging to slope-intercept form:
   • 3y = -2x - 12
   • y = (-2/3)x - 4
   • Slope = -2/3

5. Fifth Equation: 2x - y = 7

   • Rearranging to slope-intercept form:
   • y = 2x - 7
   • Slope = 2

6. Sixth Equation: 3x - 4y = -8

   • Rearranging to slope-intercept form:
   • 4y = 3x + 8
   • y = (3/4)x + 2
   • Slope = 3/4

Analyze the Pairs of Lines

1. Lines 1 and 2:

   • Slopes: 14 and -4
   • Not parallel or perpendicular (product is not -1)
   • Intersecting

2. Lines 1 and 3:

   • Slopes: 14 and -23
   • Not parallel or perpendicular (product is not -1)
   • Intersecting

3. Lines 1 and 4:

   • Slopes: 14 and -2/3
   • Not parallel or perpendicular (product is not -1)
   • Intersecting

4. Lines 1 and 5:

   • Slopes: 14 and 2
   • Not parallel or perpendicular (product is not -1)
   • Intersecting

5. Lines 1 and 6:

   • Slopes: 14 and 3/4
   • Not parallel or perpendicular (product is not -1)
   • Intersecting

6. Lines 2 and 3:

   • Slopes: -4 and -23
   • Not parallel or perpendicular (product is not -1)
   • Intersecting

7. Lines 2 and 4:

   • Slopes: -4 and -2/3
   • Not parallel or perpendicular (product is not -1)
   • Intersecting

8. Lines 2 and 5:

   • Slopes: -4 and 2
   • Not parallel or perpendicular (product is not -1)
   • Intersecting

9. Lines 2 and 6:

   • Slopes: -4 and 3/4
   • Not parallel or perpendicular (product is not -1)
   • Intersecting

10. Lines 3 and 4:

    • Slopes: -23 and -2/3
    • Not parallel or perpendicular (product is not -1)
    • Intersecting

11. Lines 3 and 5:

    • Slopes: -23 and 2
    • Not parallel or perpendicular (product is not -1)
    • Intersecting

12. Lines 3 and 6:

    • Slopes: -23 and 3/4
    • Not parallel or perpendicular (product is not -1)
    • Intersecting

13. Lines 4 and 5:

    • Slopes: -2/3 and 2
    • Not parallel or perpendicular (product of slopes = -4/3, not -1)
    • Intersecting

14. Lines 4 and 6:

    • Slopes: -2/3 and 3/4
    • Not parallel or perpendicular (product of slopes = -1/2, not -1)
    • Intersecting

15. Lines 5 and 6:

    • Slopes: 2 and 3/4
    • Not parallel or perpendicular (product is not -1)
    • Intersecting

Conclusion

All pairs of lines analyzed above are Intersecting.

You may ask for specific line pairs if you need more details.