## How to solve algebra slope

**Introduction :**

In algebra, the slope is defined as the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line. Given two points (

*x*1,

*y*1) and (

*x*2,

*y*2) on a line, the slope

*m*of the line is,

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

**(Source – Wikipedia)**

Example problems for algebra slope:

**Algebra formulas to find slope of the line is,**

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

1. Solve the slope of the line which passes through points (-3, 7) and (6, 10).

**Solution:**

**x1 = -3 ; y1 = 7**

**x2 = 6 ; y2 = 10**

**Slope of the line is (m) =**`(y2-y1)/(x2-x1)`

**= `(10-7) /( 6-(-3))`**

= `(3/9)`

= `1/3`

2.Solve the slope of the line which passes through points (6, 2) and (12, 5).

**Solution:**

**x1 = 6 ; y1 = 2**

**x2 = 12 ; y2 = 5**

**Slope of the line is (m) =**`(y2-y1)/(x2-x1)`

**= `(5-2) /(12-6)`**

= `(3/6)`

= `1/2`

3.Solve the slope of the line, which is perpendicular to the line y = -x + 2.

**Solution:**

**Given:**

**y = -x + 2 (y = mx + b)**

Slope (m2) = -1

If two lines are perpendicular then their slope will be

m1 x m2 = -1

m1 x -1 = -1

m1 = -1/-1

m1 = 1

**Slope of the line (m1) = 1**

4.Solve the slope of the line, which is parallel to the line y = 3x + 7.

**Solution:**

**Given:**

**y = 3x+ 7 (y = mx + b)**

Slope (m2) = 3

If two lines are parallel to each other, then their slope will be equal

m1 = m2

therefore,

m1 = 3

**Slope of the line (m1) = 3**

Practice problem for algebra slope:

- Solve the slope of line which passes through points (-8, 14) and (4, 7)

**Answer: slope = `-7/12`**

2.Solve the slope of the line which passes through points (6, 4) and (8, 5).

**Answer: slope = `1/2`**

3.Solve the slope of the line, which is perpendicular to the line y = 3x + 5

**Answer: slope = `-1/3`**