For each linear equation the procedure is the same:
Suppose the equation is y = mx + c where x and y are the two variables and m and c are two constants.
Set x = 0 so that the equation becomes y = c. Mark the point P = (0, c) on the coordinate plane.
Set y = 0 so the equation becomes 0 = mx + c so that x = -c/m. Mark the point Q = (-m/c, 0) on the plane.
Join PQ with a straight line and extend in both directions.
You may wish to select another value of x (or y), substitute into the equation and solve. This will give the coordinates of a third point, R. The only reason for doing this is that if R is not on the line PQ then you know you have made a mistake.
Repeat for other equations.
true
The answer will depend on the variables plotted on the graph!
Yes, the graph of a linear equation can be a line. There are special cases, sometimes trivial ones like y=y or x=x which are linear equations, but the graph is the entire xy plane. The point being, linear equations most often from a line, but there are cases where they do not.
That there is a linear relationship between the dependent and independent variables
straight line
The statement "A system of linear equations is a set of two or more equations with the same variables and the graph of each equation is a line" is true.
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.
true
Because its linear and the equation is a problem to solve
The answer will depend on the variables plotted on the graph!
One of the most common ways to represent linear equations is to use constants. You can also represent linear equations by drawing a graph.
A bivariate linear inequality.
Yes, the graph of a linear equation can be a line. There are special cases, sometimes trivial ones like y=y or x=x which are linear equations, but the graph is the entire xy plane. The point being, linear equations most often from a line, but there are cases where they do not.
Assuming you work with two variables (like x and y) only: if the graph is a vertical line, e.g. x = 5, then it is not a function. Otherwise it is.
That there is a linear relationship between the dependent and independent variables
When you graph a linear equation, you make a line. A line continues infinitely.
straight line