X-Intercept: The point where a line crosses the x-axis.


Example:(1)
\begin{align} y=\frac{x^2+3x+2}{x-1} \end{align}

Step 1: Factor the numerator

(2)
\begin{align} \frac{(x+2)(x+1)}{(x-1)} \end{align}

Step 2: Set the factors equal to zero

(3)
\begin{equation} x+2=0, x+1=0 \end{equation}

Step 3: Solve for x

(4)
\begin{equation} x=-2, x=-1 \end{equation}

X intercept: -1,-2

Y-Intercept: The point or points that a line crosses the y axis.
In standard form, the y-intercept is

(5)
\begin{align} \frac{constant}{constant}\ \end{align}

Example:

(6)
\begin{align} \frac{2x^2+5x-3}{2x^2+7+3}\ \end{align}
(7)
\begin{align} \frac{-3}{3}=-1 \end{align}

Y Intercept: -1