# What is the slope and intercept for x=9?

Nov 1, 2016

The line has an infinite slope and there is no y intercept, only an x intercept at $\left(9 , 0\right)$.

#### Explanation:

This is the equation of a vertical line.

The slope of a line is defined as the change in y divided by the change in x so

slope = (Deltay)/(Deltax) = ( y_2 - y_1)/(x_2 - x_1

${x}_{1} = 9$

${x}_{2} = 9$

$9 - 9 = 0 \text{ }$ Dividing by zero equals infinity or is undefined. so

$\frac{{y}_{2} - {y}_{1}}{0}$ = infinity, an undefined value.

( try dividing by zero on a calculator)

Also since the line goes straight up from the point $\left(9 , 0\right)$ it will never cross the y-axis, hence there is no y-intercept.