After learning the definitions and concepts of proportional and inversely proportional in mathematics, the next step to study is linear functions. Similar to the graph of direct proportionality, 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. The shape of the graph will change depending on what number of slopes and intercepts are used. Linear functions also require us to write graphs and create linear equations from them.

There are also many problems to find the intersection, in which case we can use simultaneous equations to find the intersection point.

Linear functions are almost identical to the concept of direct proportionality. Therefore, we frequently use linear functions in our daily life. We will explain how to solve problems with linear functions.

## Linear functions Are Special Proportional

There is often a relationship between direct proportionality. Therefore, we frequently use proportional in everyday life. Another concept that is also essential in everyday life is linear functions. Proportional and linear functions are similar, and all people use linear functions in everyday life.

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 proportional formula 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 want to save money from zero savings, it becomes a linear equation like this On the other hand, if you already have some savings, you have to take into account the amount of savings. 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.

Think of linear functions as a special case of proportional. Linear functions are proportional that start from a specific point, rather than starting from zero.

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

The formula for direct proportionality is $y=ax$. The formula for linear functions, on the other hand, is $y=ax+b$. Because it starts at a specific point, we add $+b$ to the formula of proportional.

## Create and Solve an Equation for Linear Functions

A very similar field to direct proportionality is linear functions. Think of linear functions in mathematics as a special case of a proportional.

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 must find the slope and intercept to create an equation.

In linear functions, there are also many graph-based problems. 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 we understand the properties of these linear functions, we will be able to solve word problems. If you can solve word problems, you will be able to use mathematics in all aspects of your daily life.