A linear equation is an equation in which the power of the variables is always 1. Here we will discuss the concept of x- intercept, y-intercept, and the standard form of a line. Check out the solved examples to understand the steps involved in graphing linear equations . Read More Read Less
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A linear equation is defined as an equation in which all the variables have an exponent of 1 . When this equation is graphed, we can observe that it will always be in the form of a straight line.
There are two forms of representing a linear equation:
A linear equation with one variable is a single-variable equation. \(Ax~+~B~=~0\) , is the standard form of a linear equation in one variable.
A linear equation in two variables written in the standard form is, \(Ax~+~By~=~C\) .
In the equation for two variables, x and y are variables, A and B are non-zero coefficients, and C is a constant.
The slope of a line indicates the steepness of a line. When a line has a positive slope, it moves upward from left to right. When moving from left to right, a line with a negative slope moves downward . Two linear functions are parallel if their slopes are the same.
The slope of a line can be calculated as the ratio of the difference between the y-coordinates, to the difference between the x-coordinates of any two points lying on the line.
The difference between the y-coordinates is called the rise , and the difference between the x-coordinates is called the run . Hence, the slope is the ratio of the rise to the run.
The slope-intercept form of a line with a slope \(“m”\) and a y-intercept \(“b”\), or (0,b) has the equation \(y~=~mx+b\) .
A horizontal line passing through \((a,~b)\) has an equation of the form \(y~=~b\) . A vertical line passing through \((a,~b)\) has an equation of the form \(x~=~a\) .
