Finding Intercepts

Introduction for finding intercepts:

In coordinate geometry, the y-intercept is the y-value of the point where the graph of a function or relation intercepts the y-axis of the coordinate system. If the curve in question is given as y = f(x), the y-intercept is found by calculating f(0). Functions which are undefined at xy-intercept. Some 2-dimensional mathematical relationships such as circles, ellipses, and hyperbolas can have more than one y-intercept. Because functions associate x values to no more than one y value as part of their definition, they can have at most one y-intercept.                                                  Source – Wikipedia.



The general rules for finding intercepts:


Rule for finding X intercepts:

To find an x-intercept, put y = 0 in the equation.

Your x-intercept will be written as a point (x, 0).

Rule for finding Y intercepts:

To find a y-intercept, x = 0 in the equation. Your y-intercept will be written as a point (0, y).

There are two special types of lines are to be considered these are horizontal lines and vertical lines.

1. A horizontal line is in the form y = k; that is, the y-value is always a constant value.

2. A vertical line is in the form x = h; that is, the x-value is always a constant value.


Examples for finding X and Y intercepts:

Examples for finding X and Y intercepts are given below:

1) find the x Intercept in an equation y = 5x-1.

Solution:

Let the given equation is y = 5x-1.

We have to put y = 0 in the above equation

Y = 5x-1

0 = 5x-1

Add 1 on the both sides

0+1 = 5x-1+1

1 = 5x

1/5 = x

Therefore the x-intercept is (1/5, 0)

Example 2

Find the x intercept for x=2y+3

To find the x - intercept:

Solution:

We have to put y=0 in the above equation

X = 2y+3

X = 2(0) + 3

X = 0 + 3

X = 3

Therefore the x-intercept is (3, 0)

3. To find the y - intercept for y= 5x-1

Solution:

We have to put x = 0 in the above equation

Y = 5x-1

Y = 5(0)-1

Y = 0-1

Y = -1

Therefore the y-intercept is (0,-1).

4)find the y – intercept for x = 2y + 3

Solution:

We have to put x = 0 in the above equation

X = 2y+3

0 = 2y+3

-3 = 2y+3-3

-3 = 2y

Y = -3/2

Therefore the y-intercept is (0,-3/2).