The graphical concept of x- and y-intercepts is pretty simple. The x-intercepts are where the graph crosses the x-axis, and the y-intercepts are where the graph crosses the y-axis. X-intercept of a line gives the idea about the point which crosses x-axis.
Same way, y-intercept is a point at which the line crosses the y-axis. One can find out only one intercept at a time in a given equation.
The x-intercept of a line is the point at which the line crosses the x axis. ( i.e. where the y value equals 0 )
\[\large x-intercept = (x, 0)\]
The y-intercept of a line is the point at which the line crosses the y axis. ( i.e. where the x value equals 0 )
\[\large y-intercept = (0, y)\]
Solved examples of X and Y Intercept
Example: Find the x- and y-intercepts of $25x^{^{2}}+4y^{^{2}}=9$
Solution
Using the formula of the intercepts to find Xand Y Intercept separately
x-intercept:
y=0 for the x-intercept, so:
$25x^{^{2}}+4y^{^{2}}=9$
$25x^{^{2}}+4\left (0\right)^{2}=9$
$25x^{^{2}}+0=9$
$x^{2}=\frac{9}{25}$
$x^{2}=\pm \frac{3}{5}$
Then the x-intercepts are the points $\frac{3}{5}, 0$ and $\frac{-3}{5}, 0$
y-intercept:
x=0 for the y-intercept, so:
$25x^{^{2}}+4y^{^{2}}=9$
$25\left ( 0 \right )^{2}+4y^{2}=9$
$0+4y^{2}=9$
$y^{2}=\frac{9}{4}$
$y=\pm \frac{3}{2}$
The the y-intercepts are the points $\left(0,\frac{3}{2}\right)$ and $\left(0,\frac{-3}{2}\right)$