**Slope of the line :**

It is the change in y for a unit change in x along the line and usually denoted by the letter "m"

Slope is sometimes referred to as "Rise over run"

Because the fraction consists of the "rise" (the change in **y**, going up or down) divided by the "run" (the change in x, going from left to the right).

The figure given below illustrates this.

From the above figure, the slope of the straight line joining the points A (x₁, y₁) and B (x₂, y₂) is

That is,

If the equation of a straight line given in general form

ax + by + c = 0,

then, the formula to find slope of the line is

**Let **θ be the angle between the straight line "l" and the positive side of x - axis.

The figure given below illustrates this.

Then, the formula to find slope of the line is

**m = tan θ**

In the general form of equation of a straight line

ax + by + c = 0,

(i) if "x" term is missing, then the line will be parallel to x - axis and its slope will be zero.

We know that slope = change in y / change in x

In the above figure, the value of "y" is fixed and that is "k"

So, there is no change in "y" and change in y = 0

Slope = 0 / change in x

**Slope = 0 **

(i) if "y" term is missing, then the line will be parallel to y - axis and its slope will be undefined.

We know that slope = change in y / change in x

In the above figure, the value of "x" is fixed and that is "c"

So, there is no change in "x" and change in x = 0

Slope = change in y / 0

**Slope = Undefined **

Slope of the coordinate axes "x" and "y".

(i) Slope of "x" axis zero.

(ii) Slope of "y" axis undefined.

When we look at a straight line visually, we can come to know its slope easily.

To know the sign of slope of a straight line, always we have to look at the straight line from left to right.

The figures given below illustrate this.

**Problem 1 :**

Find the angle of inclination of the straight line whose slope is 1/√3

**Solution :**

Let θ be the angle of inclination of the line.

Then, slope of the line, m = tan θ

Given : Slope = 1/√3

So, we have

tan θ = 1/√3

θ = 30°

**Hence, the angle of inclination is 30° **

**Problem 2 :**

Find the slope of the straight line passing through the points (3, -2) and (-1, 4).

**Solution :**

Let (x₁, y₁) = (3, -2) and (x₂, y₂) = (-1, 4)

Then, the formula to find the slope,

m = (y₂ - y₁) / (x₂ - x₁)

Plug (x₁, y₁) = (3, -2) and (x₂, y₂) = (-1, 4)

m = (4 + 2) / (-1 - 3)

m = - 6 / 4

m = - 3 / 2

**Hence, the slope is -3/2**

**Problem 3 :**

Using the concept of slope, show that the points A(5, -2), B(4, -1) and C(1, 2) are collinear.

**Solution :**

Slope of the line joining (x₁, y₁) and (x₂, y₂) is,

m = (y₂ - y₁) / (x₂ - x₁)

Using the above formula,

Slope of the line AB joining the points A (5, - 2) and B (4- 1) is

= (-1 + 2) / (4 - 5)

= - 1

Slope of the line BC joining the points B (4- 1) and C (1, 2) is

= (2 + 1) / (1 - 4)

= - 1

Thus, slope of AB = slope of BC.

Also, B is the common point.

**Hence, the points A , B and C are collinear.**

**Problem 4 :**

Find the slope of the straight line 3x - 2y + 7 = 0.

**Solution :**

When the general form of equation of a straight line is given, the formula to find slope is

m = - coefficient of x / coefficient of y

In the given line 3x - 2y + 7 = 0,

coefficient of x = 3 and coefficient of y = - 2

Slope, m = (-3) / (-2) = 3/2

**Hence, slope of the given line is 3/2. **

**Problem 5 :**

If the straight line 5x + ky - 1 = 0 has the slope 5, find the value of "k"

**Solution :**

When the general form of equation of a straight line is given, the formula to find slope is

m = - coefficient of x / coefficient of y

In the given line 3x - 2y + 7 = 0,

coefficient of x = 3 and coefficient of y = k

Slope, m = -5 / k

Given : Slope = 5

So, we have 5 = -5/k

5k = -5

k = -1

**Hence, the value of "k" is -1. **

After having gone through the stuff given above, we hope that the students would have understood "Slope of a line".

Apart from the stuff given above, if you want to know more about "Slope of a line", please click here

Apart from the stuff, "Slope of a line", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**