y intercept

Introduction :

Y-interceptis the point where the curve crosses or touches the y axis.The equationcan touch the Y-axis more than once, some times it may not cut the y axis also, so for a given equation there can be 0 or more number of y intercepts.  Y intercept is represented by (X,Y) coordinates, where X="0" always, since the point lies on Y- axis. to find Y-intercepts we plug in 0 for X in the given equation. The following diagram shows the yintercepts.

yintercept

Inthe graph shown above, we have three functions f(x), g(x) and h(x). Both f(x) and g(x) have y intercepts and h(x) has no y -intercept.


Procedure to find y intercept and some problems


To find the Y-intercept, we follow the steps:

step1: Plug in x="0" in given equation

step 2: Solve for y

step 3: After solving for y write coordinates in the form of (0,y)

To find the X intercept we have to plug in y = 0

To find the Y intercept we have to plug in x = 0.

The general form of a straight line is y = mx +b, here b is the Y intercept.

The intercept system call will be in the form of a line is `x/a` + `y/b` = 1, here a is the X intercept and b is the Y intercept

In general, if the equation for system of intercept call to the line is ax + by = c, the X intercept is `c/a` and the Y intercept is `c/b` .


Ex:1 Find y intercepts for the equation 2x+3y-7=0

step1: Substitute x="0" in the given equation

The equation can be written as 2x+3y=7

2(0)+3y=7

3y=7

y=7/3

so, y-intercept for the given equation is (0,7/3)


Ex:2 Find the Y Intercept for equation (y-2)2= 2x+4

plug in x="0

(y-2)2= 2(0)+4

(y-2)2= 4

(y-2)= + sqrt(4) or - sqrt(4)

y - 2 = 2  or y - 2 = -2

y = 4  or y = 0

y-intercepts are: (0,0)(0,4)


Problems:


1.Find Y- intercept(s) for the following equations.

i. x+y=1

ii.2x+7y=9

iii.y2+x2=4

iv.(y-4)2+(x-5)2= 7