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In class, my math teacher was teaching us how to draw functions on a coordinate plane, and he mentioned something about the Y-Intercept being an important step in creating/solving a function. But, what exactly is a Y-Intercept?

Scribblenautical
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  • It's where the function intersects the $y$-axis. I.e. where $x = 0$. – Daniel Donnelly Oct 15 '13 at 22:26
  • The function intersects the $y$-axis as a subset of points of $\mathbb{R}^2$. Say if $f : \mathbb{R} \to $ itself. The graph of $f$ is ${(x, f(x)) : x \in \mathbb{R} }$ and the $y$-axis is defined as the subset ${(0, y) : y \in \mathbb{R} }$. Intersect the two sets. Since $f$ is a function, by definition there is one and only one point in the intersection. – Daniel Donnelly Oct 15 '13 at 22:28

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The $y$-intercept of a function $f(x)$ is the point where the function intersects the $y$-axis (if in fact it does intersect the $y$-axis) and it is found by evaluating $f(0)$, i.e., finding the value of $f(x)$ when $x = 0$.

For example,

  • the line $f(x) = y = 3x + 2$ intersects the $x$-axis at when $x = 0$:
    when $\;y = 3\cdot 0 + 2 = 2$. This is the function's y-intercept.

  • The parabola $f(x) = y = 2x^2 + 8$ intersects the $y$-axis when $x = 0:\;$
    when $\;y = 2(0)^2 + 8 = 8$. This is the function's y-intercept.

amWhy
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