Changes

In '''mathematics''' a gradient is the rate a function increases.

In [[mathematics]], a '''gradient''' is the rate a [[function]] increases.

If a function has value <math>f(a)</math> at <math>x=a</math> and <math>f(b)</math> at <math>x=b</math> with <math>a<b</math> than the gradient of <math>[a,b]</math> is,

If a function has value <math>f(a)</math> at <math>x=a</math> and <math>f(b)</math> at <math>x=b</math> with <math>a<b</math> than the gradient of <math>[a,b]</math> is,

:<math>\mathrm{gradient}=\frac{\mathrm{rise}}{\mathrm{run}}</math>,

:<math>\mathrm{gradient}=\frac{\mathrm{rise}}{\mathrm{run}}</math>,

the rise being defined as the difference between the highest point and the lowest point, negative if the highest is on the left and positive if the highest point in on the right. The run is defined as difference of the right <math>x</math>-value and the left <math>x</math>-value (see [[Cartesian coordinents]]).

the rise being defined as the difference between the highest point and the lowest point, negative if the highest is on the left and positive if the highest point in on the right. The run is defined as difference of the right <math>x</math>-value and the left <math>x</math>-value (see [[Cartesian coordinates]]).

This concept is usually first introduced with the introduction of [[linear equation]]s. The equation of a straight line in Cartesian coordinents is given by,

This concept is usually first introduced with the introduction of [[linear equation]]s. The equation of a straight line in Cartesian coordinates is given by,

:<math>y=mx+c</math>

:<math>y=mx+c</math>

where <math>m</math> is the gradient of the line and <math>c</math>is the value of the <math>y</math> coordinent when <math>x=0</math>, this is called the '''y-intercept''', e.g, where the line intercepts the <math>y</math>-axis.

where <math>m</math> is the gradient of the line and <math>c</math> is the value of the <math>y</math> coordinate when <math>x=0</math>, this is called the [[y-intercept]], e.g, where the line intercepts the [[y-axis]].

[[Category:mathematics]]

[[Category:mathematics]]