Question

write the equation of the line that passes through the points (5,-9) and (5,8) put your answer in fully reduced point-slope form unless it is a vertical or horizontal line

Answer 1

Answer: the slope is undefined. The equation of the line is x=5

Step by step

First we will find slope

(5, -9) (5, 8)

y2 - y1 over x2 - x1

8 - -9 over 5 - 5 = 17/0 undefined

This means x = 5 a vertical line because no Matter what y is, x will always = 5 and it’s a vertical line

Answer 2

The point-slope form of the equation of a line is given as per below;

`y-y_1=m(x-x_1)`

where m = slope.

Let's go ahead and find the slope of the line using the below equation;

`m=(y_2-y_1)/(x_2-x_1)`

From the question, we know that x1 = 5, x2 = 5, y1 = -9 and y2 = 8.

So let's substitute these values into the above equation and find the slope;

We can see that the slope of the line is undefined. So it means that the line is a vertical line because x2-x1 = 0.

Our equation will now be y = -9

NB: Vertical lines always have undefined slope while horizontal lines always have their slope to be equal to zero.