Standard Form
When a polynomial is arranged from greatest exponent to least exponent
Standard form refers to the form in which a mathematical equation or expression is written by arranging the terms in a specific order. In the context of linear equations, standard form refers to the way the equation is written with all variables on one side and constants on the other side.
The standard form of a linear equation in two variables can be written as follows:
ax + by = c
Where a, b, and c are constants, x and y are variables, and a and b are not both zero.
The main advantage of writing an equation in standard form is that it makes it easy to identify the x and y intercepts of the equation. The x-intercept is the point on the line where it intersects with the x-axis, which can be found by setting y=0 in the equation and solving for x. The y-intercept is the point where the line intersects with the y-axis, which can be found by setting x=0 and solving for y.
Another advantage of standard form is that it makes it easier to graph a linear equation using slope-intercept form. The slope-intercept form of a linear equation can be written as:
y = mx + b
Where m is the slope of the line and b is the y-intercept. To convert an equation in standard form into slope-intercept form, we can solve it for y:
ax + by = c
by = -ax + c
y = (-a/b)x + (c/b)
By comparing this equation with y = mx + b, it is clear that the slope of the line is -a/b and the y-intercept is c/b.
Therefore, standard form is an important concept in mathematics that is used to write equations in a specific format for ease of analysis and manipulation.
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