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A directly proportional graph has an equation of the form y = mx. It always passes through the origin.
A linear graph will have an equation in the from y = mx + c. This has a y-intercept at (0, c). It doesn't pass through the origin unless c = 0. The directly proportional graph is a special case of a linear graph.
What else can I help you with?
How are linear equations and functions alike?
They are not. A vertical line is not a function so all linear equations are not functions. And all functions are not linear equations.
Do linear graphs represent proportional relationships?
Do all linear graphs have proportional relationship
Do all graphs of linear equations have x intercepts?
YES, all linear equations have x-intercepts. because of the x, y has to be there 2!
What does it mean for a system of linear equations to have no solutions?
It means that there is no set of values for the variables such that all the linear equations are simultaneously true.
Why are linear equations called linear equations?
Because, if plotted on a Cartesian plane, all solutions to the equation would lie on a straight line.
Are linear equations and functions different?
All linear equations are functions but not all functions are linear equations.
How are linear equations and functions alike?
They are not. A vertical line is not a function so all linear equations are not functions. And all functions are not linear equations.
Are all linear equations functions Is there an instance when a linear equation is not a function?
Linear equations are always functions.
Do linear graphs represent proportional relationships?
Do all linear graphs have proportional relationship
What are the linear systems?
A "system" of equations is a set or collection of equations that you deal with all together at once. Linear equations (ones that graph as straight lines) are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables.
Do all graphs of linear equations have x intercepts?
YES, all linear equations have x-intercepts. because of the x, y has to be there 2!
What does it mean for a system of linear equations to have no solutions?
It means that there is no set of values for the variables such that all the linear equations are simultaneously true.
Is linear algebra and linear equations the same?
Linear Algebra is a branch of mathematics that enables you to solve many linear equations at the same time. For example, if you had 15 lines (linear equations) and wanted to know if there was a point where they all intersected, you would use Linear Algebra to solve that question. Linear Algebra uses matrices to solve these large systems of equations.
Why are linear equations called linear equations?
Because, if plotted on a Cartesian plane, all solutions to the equation would lie on a straight line.
What is the parent function for ALL linear equations?
y = x
Which best describes a system of equations that has no solution?
An "inconsistent" set of equations. If they are all linear equations then the matrix of coefficients is singular.
What is a system of linear equations?
A system of linear equations determines a line on the xy-plane. The solution to a linear set must satisfy all equations. The solution set is the intersection of x and y, and is either a line, a single point, or the empty set.
