what is the equation of a line that passes through (-7, 3) and is perpendicular to -5/3x = 1/4y -8

Select all answers that apply
Y = 3/20x + 81/20
Y-3 = 3/20(x+7)
Y-3 = -20/3(x+7)
Y = -20/3x -32
3x -20y = -81
The answer can be anything thing that occurs during solving the problem or is the answer.

Answer:

The 1st, 2nd and 5th options are correct.

Step-by-step explanation:

The equation of a line can be written in the form of y=mx+c, where m is the gradient and c is the y-intercept.

①Rewrite the given equation into the form of y=mx+c to find the gradient.

[tex]- \frac{5}{3} x = \frac{1}{4} y - 8 \\ \frac{1}{4} y = - \frac{5}{3} x + 8 \\ y = - \frac{20}{3} x + 32[/tex]

Thus, the gradient of the given equation is [tex] - \frac{20}{3} [/tex].

② Find gradient of unknown line.

The product of the gradients of perpendicular lines is -1.

Let m be the gradient of the unknown line.

[tex]- \frac{20}{3} m = - 1 \\ m = - 1 \div ( - \frac{20}{3} ) \\ m = - 1 \times ( - \frac{3}{20} ) \\ m = \frac{3}{20} [/tex]

③Substitute the value of m into the equation.

[tex]y = \frac{3}{20} x + c[/tex]

④ Find the value of c by substituting a pair of coordinates.

When x= -7, y= 3,

[tex]3 = \frac{3}{20} ( - 7) + c \\ 3 = - \frac{21}{20} + c \\ c = 3 + \frac{21}{20} \\ c = 4 \frac{1}{20}[/tex]

Thus, the equation of the line is [tex]y = \frac{3}{20} x + 4 \frac{1}{20} [/tex].

Thus, the 4th option is incorrect.

Writing c as an improper fraction,

[tex]y = \frac{3}{20}x + \frac{81}{20} [/tex]

Thus, the 1st option is correct.

-3 from both sides of the equation:

[tex]y - 3 = \frac{3}{20} x + \frac{21}{20} [/tex]

Factorise 3/20 out of the right hand side:

[tex]y - 3 = \frac{3}{20} (x + 7)[/tex]

Thus, the 2nd option is correct.

The 3rd option is incorrect as factorising -20/3 out would leave us with -0.0225 as the coefficient of x.

Let's look at the 5th option.

[tex]y = \frac{3}{20} x + 4 \frac{1}{20} [/tex]

×20 on both sides:

[tex]20y = 3x + 81[/tex]

-20y on both sides:

[tex]3x - 20y + 81 = 0[/tex]

-81 on both sides:

[tex]3x - 20y = - 81[/tex]

Thus, the 5th option is also correct.

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