Question

Find the slope of the line passing through the points (-6-9) and (9,-9)

Find the slope of the line passing through the points (4,1) and (4,-5).

Answer 1

Hello there! We're provided with two problems in one, but we can solve each of them by using the slope formula, which is this:

`\stackrel\diamond{\boxed{\boxed{\bold{(y_2-y_1)/(x_2-x_1)}}}}`

In this formula,

• 
  `\sf{y_2=-9}`
• 
  `\sf{y_1=-9}`
• 
  `\sf{x_2=9}`
• 
  `\sf{x-1=-6}`

Plug in the values:

• 
  `\sf{(-9-(-9))/(9-(-6)) =(-9+9)/(9+6) =(0)/(15) =\boxed{0}}`

So the slope is 0.

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

The second problem can be solved the same way!

Once again, we'll use the formula

`\stackrel\diamond{\boxed{\boxed{\bold{(y_2-y_1)/(x_2-x_1)}}}}`

only this time, the values are different:

• 
  `\sf{y_2=-5}`
• 
  `\sf{y_1=1}`
• 
  `\sf{x_2=4}`
• 
  `\sf{x_1=4}`

Plug in the values:

• 
  `\sf{(-5-1)/(4-4) =(-6)/(0) =\boxed{unde fined}`

So the slope's undefined. I hope this helps, feel free to comment if you have any queries regarding the slope formula! ^^

Answer 2

9514 1404 393

Answer:

• zero
• undefined

Explanation:

The slope formula is useful for this.

m = (y2 -y1)/(x2 -x1)

__

First line:

m = (-9 -(-9))/(9 -(-6)) = 0/15 = 0

The slope of the first line is zero.

__

Second line:

m = (-5-1)/(4 -4) = -6/0 = undefined

The slope of the second line is undefined.

_____

It is always a good idea to apply a little critical thinking to the given information. Here, you observe that the y-coordinates of the first pair of points are the same. That means this is a horizontal line, with a slope of 0.

Similarly, you observe that the x-coordinates of the second pair of points are the same. That means this is a vertical line, with undefined slope.