# X and Y Intercepts

Sub Topics

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

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.

## Finding X and Y Intercepts

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 4x + 3y = 15

Solution:
Given 5
x + 3y = 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
+ 3y = 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 16x2 + 4y2 = 9

Solution:
Given
16x2 + 4y2 = 9
To find the x-intercept put y=0
=>16x2 + 4*0 = 9
=>16x2 = 9
=>x2=9/16
=>x=±3/4

To find the y-intercepts put x=0
=>16*02 + 4y2 = 9
=>4y2 = 9
=>
y2 = 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)