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Murljashka [212]
3 years ago
9

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

l that apply.
y = –x – 2
2x + 5y = −10
2x − 5y = −10
y + 4 = –(x – 5)
y – 4 = (x + 5)
Mathematics
2 answers:
natka813 [3]3 years ago
8 0
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;
Ivanshal [37]3 years ago
8 0

Answer:

Option B) 5y + 2x = -10  

Step-by-step explanation:

We are given the following information in the question:

Given equation of line:

5x-2y =-6\\y = \displaystyle\frac{-5x-6}{-2}\\\\y = \frac{5}{2}x + 3

Comparing to the slope intercept form:

y = m_1x +c_1

we get, m_1 = \displaystyle\frac{5}{2}

A line perpendicular will have a slope m_2 such that

m_1.m_2 = -1\\m_2 = \displaystyle\frac{-1}{m_1} = \frac{-2}{5}

The equation of line is given by:

(y-y_0) = m_2(x-x_0)

where m_2 is the slope of line and (x_0,y_0) 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,

(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

is the required equation of line.

Hence option B) is the correct answer.

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