Question

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).

Answer 1

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.

Answer 2

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