What is the gradient of a straight line on a graph?

A line on a graph is y = 4.





How do you write the gradient of this line?What is the gradient of a straight line on a graph?
The gradient of a straight line like y = C, where C is a constant, is always 0, because the derivative of a constant is 0. If you had a slope, like y = Cx, then it's gradient would be C, because those are the rules of the derivation (of course the rules of derivation don't happen by accident, but you'll see the proof you need if you look for it, these cases are not hard). Lines that are not straight, but have quadratic curves, for example, or have an asymptote, are more complicated, because they'll depend on the indepedent variable (well, they couldn't depend on some stupid variable that was already depedent itself...).What is the gradient of a straight line on a graph?
If the question is y=4 it means that no matter what x-value you have, the corresponding y-value will always be 4. Thus, a straight horizontal line at ';height'; 4.





Since gradient equals ';rise-over-run'; and the rise (ie. the change in height over the ';run'; distance. Since the ';height'; is always four, there is no change) is zero, the gradient is zero.





You could write your answer as: dy/dx = 0
this line has no gradient





y=mx+c where m is the gradient





a graph of y = 4 means that it is always horizontal and thus does not have a ';change in';





if u draw it and then try draw a rectangled triangle like you would for other lines with gradients, you will obv see that it cant be done :)
The generic equation of a straight line on a graph is





y=mx + c





and the gradient (or slope) of a line is simply m





In your case the equation


y=4





actually means





y = 0*x + 4


so m is zero, and that's your gradient.






This line is parallel with the y axis. Its slope is zero. (tan 0 = 0)


In standard form, y = mx +c, it is y = 0 + 4, so you can see it has a slope of zero
The gradient of the line is 0 because it is a flat line and doesn't go up or down as x changes.