# RISE OVER RUN WORKSHEETS

## About "Rise over run worksheets"

Rise over run worksheets :

Rise over run worksheets are much useful to the students who would like top practice problems on slope and equation of straight line.

Actually, the formula for slope is referred to as "rise over run".

The figure given below illustrates this.

## Rise over run worksheets - Problems

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"

## Rise over run worksheets - Answers

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 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 "Rise over run worksheets".

Apart from the stuff, "Worksheets on slope", if you need any other stuff in math, please use our google custom search here.

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