Choose the equation and the slope of the line that passes through (5,-3) and is perpendicular to the x-axis.

The equation is x = 5 ⇒ F

The slope is undefined ⇒ C

Step-by-step explanation:

* Lets talk about the slopes of the line and the relation between

 the parallel lines and the perpendicular lines

- If the two lines are parallel, then their slopes are equal

- If the two lines perpendicular, then the product of their slopes = -1

 that meas one of them is additive inverse and multiplicative

 inverse of the other

- If the line parallel to x-axis, then all the points on that line

 have the same y-coordinates (a , b) (horizontal line)

∵ The slope = (y2 - y1)/(x2 - x1)

∴ Its slope = 0 because (y2 - y1) = 0

* Its equation is y = b

- If the line parallel to y-axis, then all the points on that line

 have the same x-coordinates (a , b) (vertical line)

∵ The slope = (y2 - y1)/(x2 - x1)

∴ Its slope = undefined because (x2 - x1) = 0

* Its equation is x = a

* Now look to the problem

- The line is ⊥ x-axis means it is parallel to y-axis (vertical line)

∴ Its slope = undefined

∵ It passes through point (5 , -3)

∴ Its equation is x = 5

* The equation is x = 5

* The slope is undefined

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!

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step-by-step explanation: