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

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is