After learning the definitions and concepts of direct proportion and inverse proportion in mathematics, the next step to study is linear functions. Similar to the graph of direct proportional, it is linear functions that if the value of $x$ increases, the value of $y$ increases in the same ratio.

In linear functions, there are two concepts: slope and intercept. Depending on the slope and intercept numbers, the shape of the graph will change. Linear functions also require us to draw graphs and create linear equations from them.

There are many problems that ask for the intersection point, and in such cases, the intersection point can be found by using simultaneous equations.

The concept of linear functions is almost the same as that of direct proportions. Therefore, we often use linear function calculations in our daily lives. So we will explain how to solve problems with linear functions.

## Linear functions Are Special Proportions

There are many things that are related to proportions. For this reason, we use proportions frequently in our daily lives. Another concept that is also essential in our daily lives is linear functions. Proportions and linear functions are similar, and all of us use linear functions in our daily lives.

For example, we use linear functions when we think about our daily living expenses. It is the calculation of a linear function to figure out how much you can spend each day based on your current savings.

The formula for proportionality is $y=ax$. For example, if you get an allowance of \$20 per month and you don’t spend any money at all, your savings after$x$months will be expressed by the following equation. •$y=20x$If you save money from zero, the equation will be a linear equation like this. On the other hand, if you already have some money saved, you have to take into account the amount of money you have saved. For example, if you already have \$50 in savings, the total amount of savings after $x$ months will be following.

• $y=20x+50$

In real life, it is common to start from a specific point, rather than starting from zero. In linear functions, we create an equation that takes this into account.

Let’s think of linear functions as a special case of proportionality. A linear function is a proportion that does not start from zero but from a specific point.

### Linear Functions Have a Slope and Intercept, Resulting in the Formula $y=ax+b$

The formula for direct proportion is $y=ax$. On the other hand, the formula for a linear function is $y=ax+b$. To start from a specific point, we add $+b$ to the proportional formula.

## Create and Solve Equations for Linear Functions

A field that is similar to direct proportion is linear functions. Think of linear functions in mathematics as a special case of proportions.

There are so many situations where we have to use linear functions to make calculations. For example, when you calculate your future savings, you use linear functions. When calculating, we need to find the slope and intercept to create an equation.

Also, in linear functions, there are many problems that use graphs. So you need to be able to calculate the slope and intercept from the graph. By using coordinates, we can get an expression for a linear function. Also, by using simultaneous equations, we can find the intersection of two lines.

Once you understand the properties of these linear functions, you will be able to use mathematics in all aspects of your daily life.