Question

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

Answer 1

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.

Form of perpendicular line

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

Particular solution

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

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Additional comment

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 standard form 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.

Answer 2

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

How to find the equation of a line?

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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