Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? select three options.
y = –x – 2
2x + 5y = −10
2x − 5y = −10
y + 4 = –(x – 5)
y – 4 = (x + 5)

y+4=-(2/5)(x-5) > equation of the line into point slope form

y=-(2/5)x-2 > equation of the line into slope intercept form

2x+5y=-10 > equation of the line in standard form

Step-by-step explanation:

step 1

Find the slope of the given line

we have

5x-2y=-6

isolate the variable y

2y=5x+6

y=2.5x+3

The slope m of the given line is m=2.5

step 2

Find the slope of the line perpendicular to the given line

We know that

If two lines are perpendicular, then their slopes are inverse reciprocal each other

so

m1=5/2

the inverse reciprocal is

m2=-2/5

step 3

Find the equation of the line into point slope form

y-y1=m(x-x1)

we have

m=-2/5

point (5,-4)

substitute

y+4=-(2/5)(x-5) > equation of the line into point slope form

y=-(2/5)x+2-4

y=-(2/5)x-2 > equation of the line into slope intercept form

Multiply by 5 both sides

5y=-2x-10

2x+5y=-10 > equation of the line in standard form

step-by-step explanation:

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