Question

When dealing with an equation containing two variables, we can put the graph of the equation on the coordinate plane because the number of variables is equal to the number of dimensions that are needed to properly graph the solution. Each axis on a graph represents one variable in the equation being graphed. What would you use to graph the solution to an equation with one variable? What would you use to graph the solution to an equation with three variables? Could you graph an equation containing more than four variables? Explain. If you were given the graph of an equation with two variables on a coordinate plane, what would happen to the graph if all the y-values were increased by 1? What would happen to the graph if all the x-values were increased by 1? What would happen to the graph if all the y-values were multiplied by 2 or by 1/2? Explain.

Answer 1

What would you use to represent the solution in an equation with a variable?
 I would use the real line that goes from x belongs (-infinite, infinite).
 What would you use to represent the solution in an equation with three variables?
 To present the solution of an equation with three variables you need the XYZ coordinate system because you would generate a 3D graph because "because the number of variables is equal to the number of dimensions needed to graph the solution correctly".
 Could you graph an equation that contains more than four variables?
 It CAN NOT be done since the number of variables is equal to the number of dimensions that are needed to graph the solution correctly. Therefore, we can graph only up to three variables (three dimensions).
  If you were given the graph of an equation with two variables in a coordinate plane, what would happen to the graph if all the values ​​of y were increased by 1?
 if all the values ​​of y are increased by 1, the graph shifts by 1 unit to the right.
 What would happen to the graph if all values ​​of x were increased by 1?
 If all values ​​of x are increased by 1, the graph moves 1 unit up.
 What would happen to the graph if all the  y-values ​​were multiplied by 2 or by 1/2?
 If the values ​​of y are multiplied by 1/2 then the slope of the graph is smaller so the graph looks wider.
 If the values ​​of y are multiplied by 2 then the slope of the graph is larger so the graph looks narrower.