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Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

Slope of a line between 2 points of a line given by Δy , =
difference in vertical coordinates of 2 points

ΔX difference in the horizontal coordinate of 2 points

X = 5 is a line parallel to Vertical axis:

All points along the line X=5 have the same vertical value , their difference is always f 0 ,

then:

ΔY = 0

ΔX

Y =8 : is a line parallel with horizontal axis : all points along it have the same value of X, therefore;

the difference is always 0

Δx = 0

Δy = Δy = undefined

Δx 0

Hi Shekinah;

y=8

The slope is defined as change-of-y divided by change-of-x...

(y-y_{1})/(x-x_{1})

(8-8)/(x-x_{1})

0/(x-x_{1})

x and x_{1} can be any two points. The situation is that the sum of zero is in the numerator. The slope is defined as zero.

x=-5

(y-y_{1})/(x-x_{1})

(y-y_{1})/(-5--5)

(y-y_{1})/0

Zero is the denominator, also called the divisor. Nothing can be divided by zero. This is an undefined slope.

y = 0 is the equation of a line with 0 slope and y intercept 8.

In other words, y = mx + b ⇒ y = (0)x + 8 ⇒ y = 8.

Similarly, x = -5 is a line perpendicular to the y-axis (i.e., infinite slope) and x-intercept -5. There is no y-intercept.

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