Why is x equals 4 a verticle line on a graph?

Answer 1

The slope of a 2D graph is determined by the 'x' and 'y' values of the line, so the 'y' value here equals zero. In the equation y = mx + c, where 'm' is the gradient and 'c' is a constant (assumed here to be 0), 4m = 0, and so the gradient has to equal 0.

Note: Every line has an equation that can be expressed in the form ax + by + c = 0. But not all the lines can be expressed in the (slope-intercept) form y = mx + b. For example, x = 4 can be written as 1x + 0y - 4 = 0, but cannot be written in the slope-intercept form because its slope is undefined. When the slope of the line is 0, then the line is a horizontal line. When the slope is undefined, then the line is a vertical line. So all the points on the graph of x = 4 have a value of x that is always 4. So that for any y-coordinate, the corresponding x-coordinate for every point on the line is 4. For example, three of the points on the graph of x = 4 are (4, -3), (4, 0), and (4, 3). If you draw a line that passes through these three points, you will see that the line is a vertical line.