Question

How do you find the slope of the line that passes through (4,-1.5), (4, 4.5)?

Answer 1

`"slope is undefined"`

Explanation:

To calculate the slope use the `color(blue)"gradient formula"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))`
where m represents the slope and `(x_1,y_1),(x_2,y_2)" 2 coordinate points"`

The 2 points here are (4 ,-1.5) and (4 ,4.5)

let `(x_1,y_1)=(4,-1.5)" and " (x_2,y_2)=(4,4.5)`

`rArrm=(4.5-(-1.5))/(4-4)=6/0`

Division by zero is undefined hence the slope is undefined.

`color(blue)"Note"` that the x-coordinates of the 2 points are equal, that is both 4. This lets us know that the line is vertical and parallel to the y-axis The slope of the y-axis is undefined.

Noting this allows us to state the slope without use of the gradient formula.
graph{y-1000x+4000=0 [-10, 10, -5, 5]}