The x and y intercepts on graph is simple.x-intercepts are where x crosses the x-axis and y-intercepts are where y crosses the y-axis. If a straight line cuts the x-axis at A and y-axis at B, then OA with proper sign is called **x-intercept** and OB with proper sign is called the **y-intercept** made by the straight line.

They are usually denoted by a and b respectively and called as x and y intercepts.

Graphing x and y intercepts, x-intercepts are where y=0 and y-intercepts are where x=0 . Here some following x y intercepts example,

(a) Both the intercepts OA, OB are positive;

x-intercept is A where B=0 and y-intercept is B where A=0.

Both x and y intercepts are positive.

(b) x-intercept is negative and y-intercept is positive;

x-intercept is A where B=0 and y-intercept is B where A=0.

x-intercepts is negative and y intercepts is positive(c) Both the slope intercept forms are negative;

x-intercept is A where B=0 and y-intercept is B where A=0.

Both x and y intercepts are negative.

(d) x-intercept is positive and y-intercept is negative.

x-intercept is A where B=0 and y-intercept is B where A=0.

x-intercept is positive and y-intercept is negative.

The x-intercept is a $\Leftrightarrow$ the line passes through (a, 0)

The y-intercept is b $\Leftrightarrow$ the line passes through (0, b)

**Example for x y intercepts for finding the vertex of a parabola:** If the x-intercept is 4, the line passes through the point (4, 0) and if the Y-intercept is -8, the line passes through the point (0,-8). Again if a line passes through the point (-3, 0), then the x-intercept is -3.

The x y intercepts calculator aids students to calculate the x and y intercepts for a given equation of a line. Instead of the manual calculation , the students can enter the values in the equation and the calculator would be automatically returning the values of x and y co-ordinates for them.

Here are some example showing manual computation of x and y intercept values:

Example 1.

Find the *x* and *y* intercepts of the equation 4*x* + 3*y* = 15

Solution:

Given 5*x* + 3*y* = 15

To find the x-intercept put y=0

=>5*x* + 3**0* = 15

=>5x=15

=>x=15/5

=>x=3

To find the y-intercepts put x=0

=>5**0* + 3*y* = 15

=>3y=15

=>y=15/3

=>y=5

Hence the x-intercept is (3,0) and y-intercept is (0,5)

Example 2.

Find the *x* and *y* intercepts of the equation 16*x*^{2} + 4*y*^{2} = 9

Solution:

Given 16*x*^{2} + 4*y*^{2} = 9

To find the x-intercept put y=0

=>16*x*^{2} + 4*0 = 9

=>16*x*^{2} = 9

=>*x*^{2}=9/16

=>x=±3/4

To find the y-intercepts put x=0

=>16**0*^{2} + 4*y*^{2} = 9

=>4*y*^{2} = 9

=>*y*^{2} = 9/4

=>y=±3/2

Hence the x-intercepts are (+3/4,0) and (-3/4,0)

and y-intercepts are (0,+3/2) and (0,-3/2)