Question

What is the slope of the line passing through the following points: `(1,3) ; (1,-2)`?

Answer 1

`"slope is undefined"`

Explanation:

`"calculate the slope m using the "color(blue)"gradient formula"`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(1,3)" and "(x_2,y_2)=(1,-2)`

`rarrm=(-2-3)/(1-1)=-5/0`

`"since division by zero is undefined then slope is undefined"`

Answer 2

Slope=undefined; vertical line

Explanation:

The slope is the change in the y-coordinates over the change in x-coordinates. The formula `m=(y_2-y_1)/(x_2-x_1)` where m is the slope, shows the change from coordinates `y_1` to `y_2` and likewise for the x-coordinates. The order that you choose to input the coordinates doesn't matter as long as the corresponding coordinates don't get mixed up. We'll call `(1,3)` `(x_1,y_1)` and `(1,-2)` `(x_2,y_2)`.

`m=(-2-3)/(1-1)`
`m=(-5)/0`

The formula gives an undefined slope meaning that the line crossing the two points is vertical.