10 Real-life Examples Of Slope-intercept Form

Last Updated on October 21, 2023 by Editorial Team

Have you ever gone to a market with a set budget but ended up shopping more than required? We all have done that, haven’t we? Though, the aftermath of calculating how much extra money you spend and what is the total amount of money spent can be challenging. 

Mathematics is indeed challenging for children and adults, but even complex mathematical concepts such as slope-intercept form can be simplified with the right techniques and efforts. Real-life concepts like tracking spent or earned money, distance traveled, time taken for completing an activity, and whatnot can be easily done by slope-intercept form. 

In this article, we have covered some real-life slope-intercept form examples for a deeper comprehension of the concept and its applications in real-life. Before we get on with examples, first let’s understand what slope-intercept form is. 

Let’s begin! 

Decoding slope-intercept form 

The slope-intercept form is a widely used algebraic concept to describe a straight line’s characteristics. In simple terms, slope intercept form is a linear equation representing algebraic manipulations on a straight line that can be calculated through y=mx+b. This line can easily be represented on a graph and represents the slope and intercept characteristics. 

Narrowing down the concept more, slope or steepness is the angle that the line forms on a graph. It represents the steepness or direction. For instance, remember the kid’s poem ‘Jack and Jill went up the hill……’ the hill they went up is the slope in real-life. 

The intercept is the point where the line intersects the axis of a graph. If the line intersects the x-axis, it is called x-intercept, and if it crosses the y-axis, it will be known as y-intercept. The slope-intercept form is the most common method of representing a line on a graph and in real life. 

For instance, 

Suppose you own a small coffee shop. It took you $250 to set up the whole shop, and you plan to sell a cup of coffee for $5. Till now, you have sold 100 cups of coffee. Now, you want to calculate the profit you have gained based on each coffee sold. 

We can do it by using the slope-intercept equation: y=mx+b 

y= (5×100)- 250 

The value of y will be the profit gained, which in this example would be 250. 

Finding slope-intercept form in real life: A few examples 

The slope-intercept form is not limited to graphical representation; you will find it applied in most of your daily life activities. Let’s see real-life examples of the most commonly used mathematical concept- slope-intercept form. 

1. Cost of renting a car 

Cars are generally given for rent at a fixed price, and the additional charge for each extra day the car is used adds up to the fixed price. For instance, you rented a car for 7 days and made an initial deposit of $200. Now, you have to pay an extra $30 for every extra day you use the car, which in this case will be 7 days.

Now that your trip is over, you want to find the overall cost using the slope-intercept formula. Simply putting the values in the equation y=mx+c, where y is your total cost, m is the cost of each additional day, x is the number of days, and c is the overall cost, you can find the total amount of money. 

2. Salary paid for hourly-based jobs with the commission 

Salary at hourly paid jobs with the commission is another great real-life example of the slope-intercept form. Hourly paid jobs have a fixed price with added income for the extra hours an employee worked and the extra commission gained. The slope-intercept form can easily be used to calculate the total amount of money earned with extra effort hours and commission. 

3. Amusement park trips 

Amusement parks are fun, but keeping the budget in check while enjoying the park is important. In addition to the ticket price of amusement parks, several fun rides charge extra money that can add up to the budget. The slope-intercept form is super useful to calculate the total charge at the end of the day, including all the extra rides and events enjoyed. 

4. Calculating temperature at high altitudes 

With increasing altitudes, temperatures keep on declining, and this is the reason why at high altitudes, people struggle to breathe. Calculating the minimum temperature value that can reach during your trek is important for safety precautions, and this can be done by slope-intercept form. With increasing height, a certain temperature will keep declining from the normal temperature at ground level. Using the equation, one can find the temperature at certain heights. 

5. To find the total time of your journey or to complete any event. 

Suppose you are visiting a museum at least 2 hours from your home. Generally, you can cover 80 miles in two hours, but constant traffic delays your fun trip. Being stuck in traffic, you plan to identify the total time it will take you to reach your destination and find that slope-intercept form is at your rescue. Similarly, you can find the total time to complete any task using slope-intercept form.

6. Downloading a movie or a song 

You have put a movie on download, and now you are waiting for the download to complete so that you can start preparing your snack and enjoy a movie night. You plan to find the time left for the download so that you can begin preparing your snacks on time. The slope-intercept form is the easiest and best method to find it, so you put values in the equation and prepare your snacks accordingly. 

For instance, suppose the application says it will take 2 hours for the whole movie to download. You noticed it is downloading at a speed of 1MB per minute. The download is halfway, that is 60 MB done. Considering, y as the total, m as the time taken per MB, and x as the completed download, we can find the remaining download time (b). 

7. Studying latitudes and longitudes

Another example of the slope-intercept form is studying latitudes and longitudes to find the directions and distances between two countries, States, cities, localities, etc. Finding the exact location of places using an equation and representing it on a graph helps study the distances and directions of two places.

For instance,  you are exploring various counties using a map as a guide. The map shows you have to walk for the next 1 hour and then turn right in some latitudinal direction. Considering m, as the distance covered by you according to the map, x as the additional time spent on covering the distance, and b as the distance remaining, you can find y is the total distance covered in that hour. 

8. Speed of eating or drinking 

You are drinking a soft drink in warm weather. You were enjoying your drink when you noticed it was getting to normal temperature very fast; let’s say at 0.5 degrees temperature is dropping every 2 minutes. Your 500ml drink is not even halfway, so you need to hurry up, but how much to hurry? The slope-intercept form is a great tool to help you find so. 

9. Finding the height of your little kid

The slope-intercept form also makes assessing and recording your kid’s physical development possible. Keeping the development period constant, parents can assess the kid’s height at a certain period. For instance, at 4 months, the child’s height was 20 inches, and the child should gain 3 inches each month. Calculating the height at the end of other months is super simple using slope-intercept form. 

10. Reading your favorite novel

Another example of the slope-intercept form is the amount of time it will take to read your favorite novel. For instance, you have 600 pages to read and plan to read 200 daily. Now that the book piqued your interest, you plan to read additional pages. It takes you 3 minutes to read a page. Considering the information, you can easily calculate the total time of reading the book using slope-intercept form. 

Why is slope-intercept form important?

The slope-intercept form is a useful mathematical concept that is important in many ways. 

  • It makes complex mathematical concepts, such as applications of quadratic equations or differential equations easy to solve. 
  • Various complex domains, such as physics, economics, statistics, engineering, etc., use the slope-intercept form for simplifying complex concepts.  
  • The slope-intercept form makes the graphical representation of complex mathematical figures easy and helps you to find the relationship between two variables and the rate of change. 

Concluding thoughts 

Slope-intercept has various real-life examples. Consciously or unconsciously, we use slope-intercept daily. The concept has found its use outside of theoretical concepts, and it is a simple concept with wide practicality, making it an ideal choice for use in real-life. Children can even use math manipulatives or slope games and activities to understand the concept and its practicality better.

Leave a Comment