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2 years ago

7. Find an equation of the line containing (- 4,5) and perpendicular to the line 5x - 3y = 4.

Mathematics

2 answers:

atroni [7]2 years ago

7 0

Answer:

3x +5y = 13

Step-by-step explanation:

The equation of a perpendicular line through a given point can be obtained by swapping the x- and y-coefficients of the original line's equation, and negating one of them. The constant in the equation needs to be chosen so the equation will be true at the given point.

<h3>Form of perpendicular line</h3>

Swapping the coefficients of the given equation, we have ...

3x -5y = c . . . . . for some constant c

Negating the y-coefficient gives a perpendicular line:

3x +5y = c

<h3>Particular solution</h3>

We want the equation to be true for (x, y) = (-4, 5), so the constant needs to be ...

3x +5y = 3(-4) +5(5) = -12 +25 = 13

The equation of the perpendicular line is ...

3x +5y = 13

<em>Additional comment</em>

This process works for equations given in any form. If you start with point-slope form or slope-intercept form, some manipulation of the result may be required to get to the form you want. Standard-form or general-form equations are the easiest to apply this method to.

Note that equations in <em>standard form</em> want to have a positive leading coefficient. That is why we chose to change the sign of the y-coefficient, rather than the x-coefficient.

bagirrra123 [75]2 years ago

6 0

The equation of the line containing (- 4,5) and perpendicular to the line 5x - 3y = 4 is y = -3 / 5 x + 13 / 5

<h3>How to find the equation of a line?</h3>

The equation of a line can be represented as follows:

y = mx + b

where

m = slope
b = y-intercept

Therefore, the equation passes through (-4, 5) and perpendicular to 5x - 3y = 4

Hence,

perpendicular lines follows the rule below:

m₁m₂ = -1

Hence,

5x - 3y = 4

5x - 4 = 3y

y = 5/ 3 x - 4 / 3

m₁ = 5 / 3

5/3 m₂ = -1

m₂ = - 3 / 5

Hence,

using (-4, 5)

5 = - 3 / 5 (-4) + b

5 = 12 / 5 + b

b = 5 - 12 / 5 = 25 - 12 /5 = 13 / 5

Therefore,

y = -3 / 5 x + 13 / 5

learn more on equation of a line here: brainly.com/question/10727767

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1. The coordinate of D are (4,5) and 1. By the midpoint formula

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3 years ago

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