Question

Choose the most convenient method to graph the line x=8.

Answer 1

Answer:

the first option : vertical line passing through the x-axis at 8.

Step-by-step explanation:

x = 8

is a special case of a line equation.

it means that it contains all points for which x = 8.

so, e.g.

(8, -26), (8, - 7), (8, 0), (8, 3), (8, 57), ...

in other words, any y value is possible, but x is constant 8.

therefore, it is one vertical line going through 8 on the x-axis.

the is therefore no y-intercept.

this line equation maps all y values from -infinty to +infinity to the x value of 8. and FYI - it is therefore not a function (where each x value has exactly one assigned y value).

the slope of such a line is infinite or even more accurate undefined.

as the slope is y difference / x difference, x difference is always 0. something divided by 0 is officially undefined and often considered as infinite.

the opposite extreme is something like

y = 8

this is now the line that contains all points with y = 8.

any x-value is possible, but y is always 8.

that is a horizontal line that goes through the y-axis at 8.

and in fact, this is a function, as every x value has exactly one assigned y value (they are all 8, but that does not matter).

there is no x-intercept, of course.

and the slope is 0, as the slope is y difference / x difference, and the y difference is always 0. 0 divided by something is 0.

Answer 2

Answer:

Recognize the equation as that of a vertical line passing through the x-axis at 8