Why is it not possible to write the equation of the line through (-8,-5) and (-8,-9) in slope intercept form?

The reason why this equation can not be written in the slope-intercept form because the slope of this line is undefined.

Step-by-step explanation:

We know the slope-intercept form of line equation is

y = mx+b

where m is the slope and b is the y-intercept

Given the points

Finding the slope between (-8,-5) and (-8,-9)

(x₁, y₁) = (-8,-5)

(x₂, y₂) = (-8,-9)

slope = m = (y₂-y₁) / (x₂-x₁)

                = -9 - (-5) / -8 - (-8)

                = -9+5 / -8+8

                = -4 / 0

                = ∞

Thus, the slope = m = ∞

In other words, whatever the value of y is, the x-value always remains constant.

In other words, the line will be vertical and the slope of a vertical line will be undefined.

Thus, the equation of this line is:

x = -8

The line graph is also attached.

Therefore, the reason why this equation can not be written in the slope-intercept form because the slope of this line is undefined.