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10. Choose the correct answer. perpendicular to 'y=5/2x-6' and has the point (5,-7)

a. y= 2/5x-9

b. y= -5/2x+14

c. y= 5/2x-39

d. y= -2/5x-5​

Sagot :

Answer:

d

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{5}{2}[/tex] x - 6 ← is in slope- intercept form

with slope m = [tex]\frac{5}{2}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{5}{2} }[/tex] = - [tex]\frac{2}{5}[/tex] , then

y = - [tex]\frac{2}{5}[/tex] x + c ← is the partial equation

To find c substitute (5, - 7) into the partial equation

- 7 = - 2 + c ⇒ c = - 7 + 2 = - 5

y = - [tex]\frac{2}{5}[/tex] x - 5 ← equation of perpendicular line → d

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