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Consider the line - 5x+2y=8.

Find the equation of the line that is parallel to this line and passes through the point (-5, -3).
Find the equation of the line that is perpendicular to this line and passes through the point (-5, -3).

2 Answers

2 votes

Answer:

The parallel equation is y=
(5)/(2)x-5.

The perpendicular equation is y=
(-2)/(5)x-5.

Explanation:

First solve for y.

-5x+2y=8

2y=5x+8

y=
(5)/(2)x+4

A line is parallel if it has the same slope, but different y-intercepts.

The y-intercept of the given point is -5, so the new slope will be y=
(5)/(2)x-5

To find a perpendicular line, you find the negative reciprocal of the given slope.

So you find
(-1)/((5)/(2) ), which is equal to
(-2)/(5).

The perpendicular equation is y=
(-2)/(5)x-5.

User MSpreij
by
8.4k points
1 vote

Answer:

Explanation:

  • A straight line will be parallel to another straight line only if their slopes are equal .
  • A straight line will be perpendicular to another straight line only when the product of their slopes is -1

Part A

  • Let 's bring the function -5x+2y=8 to the standard form
  • 2y=8+5x
  • y=2,5x+4
  • A parallel line passes through a point (-5; -3); and this means
  • y=2,5x+b
  • 2,5*(-5)+b=-3
  • b=9,5
  • y=2,5x+9,5 -straight parelenai straight y=2.5x+4

Part B

  • Let 's bring the function -5x+2y=8 to the standard form
  • y=2,5x+4
  • y=kx+b And we know k*2,5=-1=> k=-0,4
  • y=-0,4x+b
  • -0,4*(-5)+b=-3
  • b=-1
  • y=-0,4x-1 - Straight perpendicular to the straight line y=2.5x+4
User Cienki
by
8.3k points

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