I need help with this geometry for my daughter

Question

I need to find the slope of the line through each pair of points

1. ( 16, 5 ) , ( 16, 15 ) 2. ( 4,11 ), ( -12 , -1 )

( 16,-11), ( -14 , -18 ) 4. ( -2, -20 ) , ( 1, -20 )

Answer 1

The slope ("m") of a line between 2 points is calculated by this equation:

where the two points are (x₁, y₁) and (x₂, y₂) [the first point has "1" subscripts and the second point has "2" subscripts to identify which is which).

In other words, you subtract the two y-values, subtract the two x-values, then divide them. Just make sure to keep them in order (whichever point you start with, keep it first for both "x" and "y")

Example: For the first two points (16, 5) and (16, 15) let's let the first point be (16, 5). That means x₁ = 16 and y₁ = 5. By default, the other point is point 2 so x₂ = 16 and y₂ = 15. So:

m = (y₂ - y₁)/(x₂ - x₁)

m = (15 - 5)/(16 - 16) = 10/0

Bad first example. The slope is "undefined" because in math, division by zero is not defined.

Example:(4, 11) and (-12 , -1)

m = (y₂ - y₁)/(x₂ - x₁)

m = (-1 - 11)/(-12 - 4) = -12/-16 = 12/16 = 3/4 so the slope is 3/4

Answer 2

When graphing lines you can use the format y=mx+b. The x and y come from your coordinate. Like question 2's coordinate (4,11), x=4 and y=11. The slope of the line is measured by the rise (change in y) over run (change in x); the variable used for slope is m. To find the slope you can use the slope formula: m=(y₂-y₁)/(x₂-x₁). To find the slope of the second problem you can write m=(-1-11)/(-12-4) which can be simplified to m= 3/4. Using the first coordinate and our slope you can plug in the numbers to the y=mx+b to make

11=(3/4)*4+b which can be reduced to 11=3+b then to b=8. The equation for the line is then y=(3/4)x+8.

Answer: #2 y=(3/4)x+8

Special Note: If m (slope) is equal to 0 divided by a number (0/5) then equation is y=(y coordinate). For example the line running through the points (2,5) and (4,5) is y=5. If the slope is a number divided by 0 (6/0) then the equation is x=(x coordinate). For example the line running through the points (16,5) and (16,15) is x=16.

Answer 3

1) (15-5)/16-16) = slope which is undefined or infinity

2) (-1-11)/(-12-4) = slope = -12/-16 = 3/4

3) ((-18+11)/(-14-16) = slope = -7/-30 = 7/30

4) ((-20+20)/(1+2) = slope = 0