Y-intercept

<h2 id="using-equations">Using equations</h2>
<p>If the curve in question is given as 
  
    
      
        y
        =
        f
        (
        x
        )
        ,
      
    
    {\displaystyle y=f(x),}
  
 the 
  
    
      
        y
      
    
    {\displaystyle y}
  
-coordinate of the 
  
    
      
        y
      
    
    {\displaystyle y}
  
-intercept is found by calculating 
  
    
      
        f
        (
        0
        )
      
    
    {\displaystyle f(0)}
  
. Functions which are undefined at 
  
    
      
        x
        =
        0
      
    
    {\displaystyle x=0}
  
 have no 
  
    
      
        y
      
    
    {\displaystyle y}
  
-intercept.
</p><p>If the function is <a href="/facts/Linear_function/Ejvy8CKy">linear</a> and is expressed in <a href="/facts/Slope-intercept_form/JfCgALwf">slope-intercept form</a> as 
  
    
      
        f
        (
        x
        )
        =
        a
        +
        b
        x
      
    
    {\displaystyle f(x)=a+bx}
  
, the constant term 
  
    
      
        a
      
    
    {\displaystyle a}
  
 is the 
  
    
      
        y
      
    
    {\displaystyle y}
  
-coordinate of the 
  
    
      
        y
      
    
    {\displaystyle y}
  
-intercept.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a>
</p>
<h2 id="multiple---------------------y--------------displaystyle-y---intercepts">Multiple 
  
    
      
        y
      
    
    {\displaystyle y}
  
-intercepts</h2>
<p>Some 2-dimensional mathematical relationships such as <a href="/facts/Circle/9fy5ggKn">circles</a>, <a href="/facts/Ellipse/1wUDnGxY">ellipses</a>, and <a href="/facts/Hyperbola/6R6ER0mY">hyperbolas</a> can have more than one 
  
    
      
        y
      
    
    {\displaystyle y}
  
-intercept. Because <a href="/facts/Function_(mathematics)/CdReEKCh">functions</a> associate 
  
    
      
        x
      
    
    {\displaystyle x}
  
-values to no more than one 
  
    
      
        y
      
    
    {\displaystyle y}
  
-value as part of their definition, they can have at most one 
  
    
      
        y
      
    
    {\displaystyle y}
  
-intercept.
</p>
<h2 id="x--------------displaystyle-x---intercepts">
  
    
      
        x
      
    
    {\displaystyle x}
  
-intercepts</h2>
<p class="note">Main article: <a href="/facts/Zero_of_a_function/mlK3dhoT">Zero of a function</a></p>
<p>Analogously, an <a href="/facts/X-intercept/mlK3dhoT">
  
    
      
        x
      
    
    {\displaystyle x}
  
-intercept</a> is a point where the <a href="/facts/Graph_of_a_function/htYX0BGX">graph of a function</a> or <a href="/facts/Relation_(mathematics)/HjblDaMy">relation</a> intersects with the 
  
    
      
        x
      
    
    {\displaystyle x}
  
-axis.  As such, these points satisfy 
  
    
      
        y
        =
        0
      
    
    {\displaystyle y=0}
  
.  The zeros, or roots, of such a function or relation are the 
  
    
      
        x
      
    
    {\displaystyle x}
  
-coordinates of these 
  
    
      
        x
      
    
    {\displaystyle x}
  
-intercepts.<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a>
</p><p>Functions of the form 
  
    
      
        y
        =
        f
        (
        x
        )
      
    
    {\displaystyle y=f(x)}
  
 have at most one 
  
    
      
        y
      
    
    {\displaystyle y}
  
-intercept, but may contain multiple 
  
    
      
        x
      
    
    {\displaystyle x}
  
-intercepts. The 
  
    
      
        x
      
    
    {\displaystyle x}
  
-intercepts of functions, if any exist, are often more difficult to locate than the 
  
    
      
        y
      
    
    {\displaystyle y}
  
-intercept, as finding the 
  
    
      
        y
      
    
    {\displaystyle y}
  
-intercept involves simply evaluating the function at 
  
    
      
        x
        =
        0
      
    
    {\displaystyle x=0}
  
.
</p>
<h2 id="in-higher-dimensions">In higher dimensions</h2>
<p>The notion may be extended for 3-dimensional space and higher dimensions, as well as for other coordinate axes, possibly with other names. For example, one may speak of the 
  
    
      
        I
      
    
    {\displaystyle I}
  
-intercept of the <a href="/facts/Current%25E2%2580%2593voltage_characteristic/wft425cq">current–voltage characteristic</a> of, say, a <a href="/facts/Diode/JyaoyGnk">diode</a>. (In <a href="/facts/Electrical_engineering/YYXW1KLW">electrical engineering</a>, 
  
    
      
        I
      
    
    {\displaystyle I}
  
 is the symbol used for <a href="/facts/Current_(electricity)/Dc1xdnUX">electric current</a>.)
</p>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Regression_intercept/5n998IhK">Regression intercept</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Weisstein, Eric W. "y-Intercept". MathWorld--A Wolfram Web Resource. Retrieved 2010-09-22. <a href="http://mathworld.wolfram.com/y-Intercept.html" target="_blank">http://mathworld.wolfram.com/y-Intercept.html</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Stapel, Elizabeth. "x- and y-Intercepts." Purplemath. Available from
    http://www.purplemath.com/modules/intrcept.htm. <a href="https://www.purplemath.com/modules/intrcept.htm" target="_blank">https://www.purplemath.com/modules/intrcept.htm</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Weisstein, Eric W. "Root". MathWorld--A Wolfram Web Resource. Retrieved 2010-09-22. <a href="http://mathworld.wolfram.com/Root.html" target="_blank">http://mathworld.wolfram.com/Root.html</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
</ol>

Y-intercept open-in-new

Y-intercept