contestada

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).

Respuesta :

Answer:

The parallel equation is y=[tex]\frac{5}{2}[/tex]x-5.

The perpendicular equation is y=[tex]\frac{-2}{5}[/tex]x-5.

Step-by-step explanation:

First solve for y.

-5x+2y=8

2y=5x+8

y=[tex]\frac{5}{2}[/tex]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=[tex]\frac{5}{2}[/tex]x-5

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

So you find [tex]\frac{-1}{\frac{5}{2} }[/tex], which is equal to [tex]\frac{-2}{5}[/tex].

The perpendicular equation is y=[tex]\frac{-2}{5}[/tex]x-5.

kamilmatematik100504

Answer:

Step-by-step 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