Gradient of a straight line worksheet worksheet is much much useful to the students who would like to practice problems on coordinate geometry.

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

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

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

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

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

**Problem 1 :**

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

**Solution :**

Let θ be the angle of inclination of the line.

Then, gradient of the line, m = tan θ

Given : Gradient = 1/√3

So, we have

tan θ = 1/√3

θ = 30°

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

**Problem 2 :**

Find the gradient 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 gradient,

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 gradient is -3/2**

**Problem 3 :**

Using the concept of gradient, 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,

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

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

= - 1

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

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

= - 1

Thus, gradient of AB = gradient of BC.

Also, B is the common point.

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

**Problem 4 :**

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

**Solution :**

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

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

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

**Problem 5 :**

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

**Solution :**

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

Gradient, m = -5 / k

Given : Gradient = 5

So, we have 5 = -5/k

5k = -5

k = -1

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

To understand and solve the problems given in the above worksheet, we have to know the stuff "gradient of a straight line".

Now, let us look at the stuff "gradient of a straight line".

**Gradient of a straight line : **

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

Gradient is also known as slope and it 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 gradient 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 gradient 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 gradient 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 gradient will be zero.

We know that gradient = 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

Gradient = 0 / change in x

**Gradient = 0 **

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

We know that gradient = 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

Gradient = change in y / 0

**Gradient = Undefined **

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

(i) Gradient of "x" axis zero.

(ii) Gradient of "y" axis undefined.

When we look at a straight line visually, we can know the sign of the gradient easily.

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

The figures given below illustrate this.

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

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

Apart from the stuff, "Gradient of a straight line worksheetyou need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM 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**