y Intercept Definition

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The place on the graph where a line intersects the y – axis is known as the y – intercept of the line. Because x – coordinate of all the points on the y – axis is zero, therefore the value of x – coordinate for y – intercept is also zero. We put the value of x equal to 0 in the equation of a line to find its y – intercept.


Example 1: Find the y – intercept for the line 2y = 6x + 3.

Solution: The first step for finding the y – intercept of the given line is to put the value of x equal to zero in the equation of the line and solve the equation for y.

2y = 6 (0) + 3

2y = 0 + 3

2y = 3 

2y / 2 = 3 / 2

y = 3 / 2

Hence the y – intercept of the line given above is (0, 3 / 2).


 

Example 2: What is the y – intercept for the equation given below:

2 x2 + 7 x – 3 y2 + 6 y = 0


Solution:  To find the y – intercepts for the given equation, we will put the value of x equal to zero and solve the equation to find the corresponding value of y.

2 (0)2 + 7 (0) – 3y2 + 6y = 0

0 + 0 – 3y2 + 6y = 0

- 3y (y - 2) = 0

- 3y = 0                                   or                     y – 2 = 0

y = 0                                                                y = 2

So the y – intercepts of the given equation are (0, 0) and (0, 2).





 

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