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This algebra 1 math tutorial from NutshellMath offers homework help in the basics of lines and their equations. Lines and linear equations are some of the most fundamental elements of algebra. All lines have an equation or equations that represent them, and every linear equation will graph into a single line. This tutorial introduces this concept and explores what information a linear equation can offer about the graph of the line it represents, and how to determine the equation of a line from given information about it. The tutorial introduces the two major forms of linear equations: slope-intercept form and point-slope form. Slope intercept form equates the dependent variable, y, to the product of the slope and the independent variable, x, plus the intercept of the dependent axis. Slope-intercept form is expressed as y=mx+b, where m is the slope and b is the y-intercept. In order to write the equation of a line slope-intercept form, it is necessary to know the y-intercept and the slope of the line. Point-slope form uses any point on the line instead of the y-intercept to write the equation. In order to write an equation of a line in point-slope form, it is necessary to know the slope and a point on the line or coordinates of any two points on the line. With either point-slope form or slope-intercept form, it is also possible to know two points on the line, and use those to find the slope. When writing equations in either form, simply plug the known values in for the proper variables.
Equations can also be used to graph lines. An easy method is to create a table of points on the line by plugging in values for the independent variable and determining the dependent value. These points can then be graphed on the coordinate plane to find the line. Minimum of two points is required to define a unique line.
It is important to remember that any given line will only have one corresponding equating in slope-intercept form, but many corresponding equations in point-slope form, as any given non-vertical line will only have one y-intercept, but infinite individual points. However, every equation in either form will only graph to form one line.
Lines and equations are fundamental aspects of algebra. The explanations and examples in this tutorial reinforce understanding of the relationships between equations and lines.
This algebra 1 math tutorial from NutshellMath offers homework help in the basics of lines and their equations. Lines and linear equations are some of the most fundamental elements of algebra. All lines have an equation or equations that represent them, and every linear equation will graph into a single line. This tutorial introduces this concept and explores what information a linear equation can offer about the graph of the line it represents, and how to determine the equation of a line from given information about it. The tutorial introduces the two major forms of linear equations: slope-intercept form and point-slope form. Slope intercept form equates the dependent variable, y, to the product of the slope and the independent variable, x, plus the intercept of the dependent axis. Slope-intercept form is expressed as y=mx+b, where m is the slope and b is the y-intercept. In order to write the equation of a line slope-intercept form, it is necessary to know the y-intercept and the slope of the line. Point-slope form uses any point on the line instead of the y-intercept to write the equation. In order to write an equation of a line in point-slope form, it is necessary to know the slope and a point on the line or coordinates of any two points on the line. With either point-slope form or slope-intercept form, it is also possible to know two points on the line, and use those to find the slope. When writing equations in either form, simply plug the known values in for the proper variables.
Equations can also be used to graph lines. An easy method is to create a table of points on the line by plugging in values for the independent variable and determining the dependent value. These points can then be graphed on the coordinate plane to find the line. Minimum of two points is required to define a unique line.
It is important to remember that any given line will only have one corresponding equating in slope-intercept form, but many corresponding equations in point-slope form, as any given non-vertical line will only have one y-intercept, but infinite individual points. However, every equation in either form will only graph to form one line.
Lines and equations are fundamental aspects of algebra. The explanations and examples in this tutorial reinforce understanding of the relationships between equations and lines.