Coordinate Plane Slope Math

 Slope in a coordinate plane:

Slope:

In mathematics the slope of the line shows the steepness of the line. Slope is also defined as rise by run. We can find the slope from the equation of the line or form the coordinates. The positive slope has + sign and negative slope has – ve sign. Here we are going to see about slope in coordinate plane.

The formula to find slope is

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

Slope in the coordinate plane is determined by rise in y axis by run in x axis.

consider the following figure.



Here the rise in y axis is -15 units

run in y axis is 30 units

Slope = `-15/30`

slope = `-1/2`

`and it can be also calculated using the coordinates from the above formula.`


Slope in a coordinate plane - Examples:


1). Find the slope of the line containing the coordinates (5, 12) and (7, 10).

Solution:

Given:

x1 = 5     x2 = 7

y1= 10    y2 = 12

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

= `(10-12) / (7 -5)`

=` -2 / 2`

m = 1

Hence the slope of the given points are m = 1

2). Find the slope of the line containing the coordinates (14, 8) and (18, 9)

Solution:

Given: x1 = 14    x2  = 18

y1 = 8      y2 = 9

Slope m = `"(y2 - y1) / (x2`

=`" ( 9 - 8 ) / ( 18 - 14 `

= `1/4`

m = `1/4`

Hence the slope of the given points m =` 1/4 `

1)Find the slope of the line having the coordinates (6, 10) and (9, 11)
Solution:

Given:            x1 = 6     x2 = 9

y1 = 10    y2 = 11

Slope   m =` (y2-y1) / (x2-x1)`

= `(11 -10) / (9 - 6)`

= `1/3`

2) Find the slope of the line having the coordinates (7, 11) and (12, 14)

Solution:

Given:            x1 = 7     x2 = 12

y1 = 12    y2 = 14

Slope   m = `(y2-y1) / (x2-x1)`

= `(14 -11) / (12 - 7)`

= `3/5`

3) Find the slope of the line having the coordinates (11, 14) and (16, 23)

Solution:

Given:            x1 = 11     x2 = 16

y1 = 14    y2 = 23

Slope   m =` (y2-y1) / (x2-x1)`

= `(23 -14) / (16 - 11)`

= `9/5`.