What are Linear Equations in One Variable?

What are Linear Equations in One Variable?

Algebra is said to be a branch of mathematics that deals with solving equations. One type of problem that algebra frequently deals with is linear equations in one variable. This type of equation is often referred to as “linear” because the graph created from this equation will be a line.

Linear equations in one variable are equations that have a line graph, or it can also be said that a linear equation is an equation defining a straight line, written in one variable notation. The power here of the variable is 1. These types of equations can be written as y=mx+b or ax+by=c, where m, b, and c are constants. A linear equation is an equation where the highest power of the variable appearing in it is one. Linear equations can be solved by using a variety of methods, and each method has its own set of steps for solving equations. 

To practice linear equations, the students should refer to the math worksheets, which have a variety of questions that will help the students learn how to solve these equations step by step. Many online platforms these days provide free worksheets. Cuemath is one such online space where the students can find a number of helpful interactive worksheets on this topic. These worksheets cover a variety of problems with detailed step-by-step explanations of the solutions for the students to refer to in case of any doubts. These are free to download and can be printed easily. Students should take advantage of such a resource to speed up their mathematical skills and thereby increase their confidence in facing math problems.

A linear equation in one variable is an equation in which the objective variable is a function of one variable only. This is often written as y = f(x). The line that’s created using this formula will always pass through the point (0,0). 

This type of equation is solved by using a method called “slope-intercept form”, where a line is written in the form: y = mx + b; b represents the y-intercept, and m represents the slope.

An intercept is defined as a point where the line passes through the axis of the given graph. When a point crosses the x-axis, that point is called the x-intercept or the horizontal intercept.

And if that point cuts the y axis, the concerning point is called the y-intercept or the vertical intercept.

The main advantage of the slope-intercept form of the equation is that it gives the two important features of a line.

  • The slope, m
  • The y-intercept of the line.

For example:

A line y=4x + 1 having slope 4, and intercept c is 1.

These equations can be solved by using the below methods:

  1. We can add, subtract, multiply or divide the given equation by the number or the expression, but this should be executed to both sides of the equation. Remember that division by zero is prohibited.
  2. We can make use of the distributive property as and when required, i.e., a(b+c) = ab + ac
  3. Move the variable to any one side of the equation.
  4. After the multiplication of the variable by the coefficient in the last, multiply both the sides of the equation with the reciprocal of the coefficient.

Linear equations in one variable are helpful in many fields; like in science, the linear models can also be described in the slope-intercept form. The regression line in statistics can be found with the help of this slope-intercept form.