Types of Linear EQUATIONS

From unProfesor we are happy to bring you an interesting math lesson, this time about equations. Specifically, we will see what are they and what types of linear equations are there. In addition, throughout the lesson we will expose examples, so that it is easier to understand and you can perform the exercises that we propose at the end. Of course, we also leave you the solutions to these exercises at the end of the article. Grab a pen and paper and let's get started!

Before talking about the types of linear equations, let's remember that an equation is the equality in which we find letters with unknown value (which we call unknowns). Therefore, solving an equation is finding the value or values ​​that make those unknowns transform the equation in an identity, that is, that the part that remains to the left of the equal gives the same number as that of the right.

This is when the concept of "linear" comes into play. What an equation is linear means you have one or more unknowns being added

each other, although each unknown can have a coefficient. If we have only one unknown, the result is specifically a number, but if we have two unknowns, the result is a straight line. These types of equations are also known as first degree equations.

exist three types of linear equations that determine ways to represent linear equations:

1. Slope - ordinate at the origin: is of the form y = mx + b, where m is the slope of the line and b is the point where the line intersects the vertical axis.
2. Point - slope: is the shape and Y = m (x - x), in which m is again the slope and the letters x and Y that are in italics are a point through which the line passes.
   
3. Standard: is of the form Ax + By = C, where A, B and C are constants.

To calculate the slope m, it is enough to have two points (x, y) on the line and do the following:

1. Subtract the x of one point minus the x of the other point.
2. Subtract the y of one point minus the y of the other point.
3. Divide the result of step 1 by the result of step 2.

Linear equations They can be used for situations such as the following:

• When an increase in one variable directly causes an increase in the other. For example, the weight of a bag of oranges and its price can be related by a linear equation, since if one goes up, the other goes up and vice versa. Being Y the expense and X the kg, we can find that: y = 2x
• When a decrease in one variable directly causes a decrease in the other. For example, if we reduce the number of babies in a family, spending on diapers is reduced. Being Y the expense and X the number of children, we can find that: y = 6x
• When an increase in one variable causes a decrease in the other variable. For example, if we increase the number of workers, the time to complete a work will decrease. Being Y the time to complete the work and X the number of workers, we can find that: y = 40x
• When a decrease in one variable causes an increase in the other variable. For example, if we decrease the speed at which we circulate with the car, we increase the time it takes to reach the destination. Being Y the distance traveled and X the speed at which we are going, we can find that: y = 5x

We will also see an example of slope calculation. If we know that a line passes through the points (3, -2) and (5, 1), we follow the steps:

1. We subtract the x's: 5 - 3 = 2.
2. We subtract the y's: -2 - 1 = -3
3. We divide 2 / -3 = -0.6666... This is our slope.

The solutions are:

1. Make the slope - ordinate equation if we know that the slope is 3 and the line intersects the vertical axis at the number -5:

y = 3x -5

2. Write the point-slope equation if we know that the slope is 7 and a point on the line is (5, 3):

y - 3 = 7(x - 5)

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