**Real life examples of a slope.:-**

Real life example of a slope are many.

The pitch of a roof, the hill slope , the drop of a river, the railroad on the climbing hill, the elevation of a gun barrel, looking up at the moon in the sky, the desert sand , the slight slope of the North pole of the earth,even the hump of a camel poses a slope.

If we look at the houses on hill side, the roofs have a slope. They are called sloping roofs. There is a calculation involved in designing the slope. The formula used is rise over run. Thar means a 6/12 roof means the roof rises 6 inches for every horizontal foot.

When we travel on a highway , we see some signs regarding the speed, the gradient etc.

6% grade the next 3 miles means the road climbs up 6 units for every 100 unit. This means there is a rise 0f 6 for every run of 100.

In other words there is a slope of 0.06

## Roads, House Pipes , Drive Ways are Slopes

Real life examples of slopes can be seen on the road.

Roads are built with a slight slope at the center to prevent the accumulation of water so that the cars do not skid.

House pipes are built so that they have a slope to drain off the water so that they do not freeze and burst in winter.

Sewer pipes must have greater slopes than water pipes.

Drive ways have enough slope to carry rain water away from the house.

Bath tubs have enough slope to thoroughly drain away the bath water.

Bathrooms are also built sloping so that the water do not stay in the bathroom to cause slip, especially for old people’s bathroom which might cause accident (fractures)

## Problem on Slope

In mathematics we have a formula y = mx + c where m is the slope and c is y intercept ( a constant)

Let us do a real life example of a slope problem.

**A man rented a car for travel for a day. The rent was $20 per day. The running rate was $0.50 per mile**.

**Solution:**

This problem can be written as y = mx +c formula.

Here Y = the total expense. $20 is constant .So it is the y intercept C

Let us assume the man covered a distance of x miles that day. Then the total cost of the distance is 0.5x

**Hence the total expense is y = mx + c = 0.5x + 20**

Hence rate of change = slope and starting value is the y intercept. he change occurs for every mile run.But the rent for the day is constant.

Hence this problem is written in slope – intercept form and calculated.

**# A sales man is paid a daily stipend of $50. His daily expenses is met by the company. They pay $25 for every mile he travels. Can you write this problem in y = mx + c formula ?**

**Solution :**

**y = mx + c**

Let us assume he travels x miles. Then he is paid 25 times x where x can change hence 25x is the slope.

His daily stipend is $50 which is a constant . Hence his total payment can be written in the form y = mx + c

In this problem y = 25x + 50

This problem is written in slope-intercept form.

Architects use the slope formula when they build buildings, Engineers use the slope of rise and run when they build over bridges. We can call the acceleration of a car as a climbing slope and deceleration of a car as climbing down slope.

The children who play in the swing feel the upward and downward slope movement.When we climb up the stairs our body bends slightly to help us climb. This is a sloping posture. Car racers use the track that is sightly banked so that they do not skid and fall off. Enen their car takes a slope posture on turning the bends. Hence slopes are found in plenty in daily life.