Respuesta :

texaschic101
3x - 5y = 6
-5y = -3x + 6
y = 3/5x - 6/5.....the slope here is 3/5. A perpendicular line will have a negative reciprocal slope. All that means is " flip  the slope and change the sign. So our perpendicular line will need a slope of -5/3....see how I flipped the slope 3/5 and made it 5/3....then I changed the sign and made it -5/3.

y = mx + b
slope(m) = -5/3
(-8,0)...x = -8 and y = 0
now we sub and find b, the y int
0 = -5/3(-8) + b
0 = 40/3 + b
-40/3 = b

so ur equation is : y = -5/3x - 40/3 or 5x + 3y = -40
abidemiokin

The equation of the line passing through point P(−8, 0) that is perpendicular to the line 3x−5y = 6 is 3y - 5x = 40

The equation of a line in point-slope form is expressed as:

[tex]y-y_0 = m(x-x_0)\\[/tex] where:

  • m is the slope
  • [tex](x_0, y_0)[/tex] is any point on the line

Given the equation 3x - 5y = 6

Rewrite in standard form:

-5y = -3x + 6

y = 3/5 x - 6/5

Slope m = 3/5

The slope of the line perpendicular to the line = -5/3

Given the point (-8, 0)

The equation of the line perpendicular will be expressed as:

[tex]y-0=-5/3(x-(-8))\\y=-5/3(x+8)\\3y=5(x+8)\\3y=5x+40\\3y - 5x = 40[/tex]

Hence the equation of the line passing through point P(−8, 0) that is perpendicular to the line 3x−5y = 6 is 3y - 5x = 40

Learn more here: https://brainly.com/question/17684243

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