why is an equation like 2x+4=10 called a linear equation in one variable when the solution is clearly a point on the number line not a line on the cartesian coo

Question

why is an equation like 2x+4=10 called a linear equation in one variable when the solution is clearly a point on the number line not a line on the cartesian coordinate plane unless all one variable linear equations are all considered vertical lines

Answer 1

Simply put, it's a linear equation because it depends linearly on its variable.  Roughly speaking, this means the graph of either side of the equation is a line.

 

To see this, you can plot the function f(x) = 2x + 4; you'll find that this is a line.

 

You can also plot the other side of the equation, 10, which is just a horizontal line; where these two lines intersect is the solution of the equation.

 

For a visual representation, see http://www.wolframalpha.com/input/?i=Plot%5B2x+%2B+4+%3D+10%5D

 

So while you're right that the solution is, in this case, a single point, the nomenclature derives from the behavior of each side of the equation: a linear equation is an equation between two lines.

Answer 2

2x + 4 = 10

2x = 6

x = 3  represents a vertical line that crosses the x-axis at (3,0). Thus, it is a linear equation.