Q: Do all graphs of linear equations have x intercepts?

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Yes - provided you allow both x and y intercepts.

All linear equations are functions but not all functions are linear equations.

Do all linear graphs have proportional relationship

Line graphs may represent equations, if they are defined for all values of a variable.

They are not. A vertical line is not a function so all linear equations are not functions. And all functions are not linear equations.

Linear equations are always functions.

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.

All direct variation graphs are linear and they all go through the origin.

It means that there is no set of values for the variables such that all the linear equations are simultaneously true.

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.

Assuming the graph is linear, all equations will follow the formula y = mx + c, where "mx" represents the gradient of the line; "c" is the y-intercept i.e. where the graph crosses the y-axis.

Because, if plotted on a Cartesian plane, all solutions to the equation would lie on a straight line.

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.

They are all represented by straight lines.

Actually not. Two linear equations have either one solution, no solution, or many solutions, all depends on the slope of the equations and their intercepts. If the two lines have different slopes, then there will be only one solution. If they have the same slope and the same intercept, then these two lines are dependent and there will be many solutions (infinite solutions). When the lines have the same slope but they have different intercept, then there will be no point of intersection and hence, they do not have a solution.

y = x

Any solution to a system of linear equations must satisfy all te equations in that system. Otherwise it is a solution to AN equation but not to the system of equations.

An "inconsistent" set of equations. If they are all linear equations then the matrix of coefficients is singular.

Linear equations come in the form y=mx+b or y=mx-b, where x and y are the variables x and y and b is a constant (like 3). All other equations are non-linear. Linear equations has a power of 1! as long as the X has a power of 1, it is a linear equation.

View all Sir William Rowan Hamilton invented the linear equation in 1843.

Because not all equations have the co-ordinates 0,0 in their data range.

They all show the values for a set of variables for different situations or outcomes.

yes yes No, vertical lines are not functions

Linear system

Linear equations can be written as y = mx + b. Any other function would be non-linear. Some linear equations are: y = 3x y = 2 y = -2x + 4 y = 3/4x - 0.3 Some non-linear functions are: f(x) = x2 y = sqrt(x) f(x) = x3 + x2 - 2

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