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Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Check all that apply.

y = –x – 2
2x + 5y = −10
2x − 5y = −10
y + 4 = –(x – 5)
y – 4 = (x + 5)

Respuesta :

Find the slope of the line first:
5x - 2y = -6,
y = (5/2)x + 3;
Since we need a line that's perpendicular, m = - (2/5).

The only equation that has the slope of this m is 2x + 5y = -10;

Answer:

Option B) [tex]5y + 2x = -10[/tex]  

Step-by-step explanation:

We are given the following information in the question:

Given equation of line:

[tex]5x-2y =-6\\y = \displaystyle\frac{-5x-6}{-2}\\\\y = \frac{5}{2}x + 3[/tex]

Comparing to the slope intercept form:

[tex]y = m_1x +c_1[/tex]

we get, [tex]m_1 = \displaystyle\frac{5}{2}[/tex]

A line perpendicular will have a slope [tex]m_2[/tex] such that

[tex]m_1.m_2 = -1\\m_2 = \displaystyle\frac{-1}{m_1} = \frac{-2}{5}[/tex]

The equation of line is given by:

[tex](y-y_0) = m_2(x-x_0)[/tex]

where [tex]m_2[/tex] is the slope of line and [tex](x_0,y_0)[/tex] is a point through which the line passes. It is given that the line passes through the point (5, −4).

Putting all the values we get,

[tex](y +4) = \displaystyle\frac{-2}{5}(x-5)\\\\5(y+4) = -2(x-5)\\5y + 20 = -2x + 10\\5y + 2x=10-20\\5y + 2x = -10[/tex]

is the required equation of line.

Hence option B) is the correct answer.

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