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Y Intercept
The yintercept is the point where the graph intersects the yaxis. To graph, any function that is of the form y = f(x) finding the intercepts is really important. There are two types of intercepts that a function can have. They are the xintercept and the yintercept. An intercept of a function is a point where the graph of the function cuts the axis.
Let us understand the meaning of the yintercept along with its formula and examples.
1.  What is YIntercept? 
2.  YIntercept Formula 
3.  YIntercept of a Straight Line 
4.  How To Find The YIntercept? 
5.  YIntercept of a Quadratic Function (Parabola) 
6.  FAQs on YIntercept 
What is Y Intercept?
The y intercept of a graph is the point where the graph intersects the yaxis. We know that the xcoordinate of any point on the yaxis is 0. So the xcoordinate of a yintercept is 0.
Here is an example of a yintercept. Consider the line y = x+ 3. This graph meets the yaxis at the point (0,3). Thus (0,3) is the yintercept of the line y = x+ 3.
YIntercept Formula
The yintercept of a function is a point where its graph would meet the yaxis. The xcoordinate of any point on the yaxis is 0 and we use this fact to derive the formula to find the yintercept. i.e., the yintercept of a function is of the form (0, y). Thus, the formula to find the yintercept is:
Y Intercept Formula
Here are the steps to find the y intercept of a function y = f(x),
 we just substitute x = 0 in it.
 solve for y.
 represent the yintercept as the point (0, y).
Here are some examples of y intercepts.
 The yintercept of y = 5×2 + 2 is, (0, 2) because when we substitute x = 0, we get y = 5(0)2 + 2 = 2.
 The yintercept of y = 5ex is (0, 5) because when we substitute x = 0, we get y = 5e0 = 5.
YIntercept of a Straight Line
A straight line can be horizontal or vertical or slanting. The y intercept of a horizontal line with equation y = a is (0, a) and the y intercept of a vertical line does not exist. Let us learn to find the y intercept of a straight line represented in different forms.
YIntercept in General Form
The equation of a straight line in general form is ax+by+c=0. For yintercept, we substitute x=0 and solve it for y.
a(0)+ by + c =0
by + c =0
y = – c/b
Thus, the yintercept of the equation of a line in general form is:(0, c/b) or c/b
yIntercept in SlopeIntercept Form
The equation of the line in the slopeintercept form is, y=mx+b. By the definition of the slopeintercept form itself, b is the yintercept of the line. You try by substituting x=0 in y=mx+b and see whether you get b as the yintercept. Thus, the yintercept of the equation of a line in the slopeintercept form is (0, b) or b.
yIntercept in PointSlope Form
The equation of the line in the pointslope form is, yy₁=m xx₁. For yintercept, we substitute x=0 and solve it for y.
yy₁ = m (0x₁ )
yy₁= – mx₁
y = y₁ – mx₁
Thus, the yintercept of the equation of a line in the pointslope form is: (0, y₁ – mx₁) or y₁ – mx₁
How To Find YIntercept?
We have derived the formulas to find the yintercept of a line where the equation of the straight line is in different forms. In fact, we do not need to apply any of these formulas to find the yintercept of a straight line. The yintercept of the polynomial function of the form y = a1xn + a2 xn1+ … + an is just its constant term an (or) (0, an).
We just substitute x=0 in the equation of the line and solve for y. Then the corresponding yintercept is y or (0, y).
Equation of Line 
Substitute x=0 and solve for y 
y intercept 
3x+5y 6=0 
3(0)+5y6 =0 5y6=0 y=6/5 
6/5 (or) (0, 6/5) 
y= 2x3 
y=2(0)3=3  3 (or) (0, 3) 
The yintercept of a function can be easily found by graphing it using the graphing calculator and locating the point where the graph cuts the yaxis. A function has only one yintercept because otherwise, it fails the vertical line test. The yintercept of the second equation of the table (y = 2x – 3) is shown in the graph below.
YIntercept of a Quadratic Function (Parabola)
The procedure for finding the yintercept of a quadratic function or the yintercept of a parabola is the same as that of a line (as discussed in the previous section). If a quadratic equation is given, substitute x = 0 and solve for y to get the y intercept.
Examples
Equation of Parabola 
Substitute 
yIntercept 
y= x2 2x 3 
y=022(0)3=3  3 (or) (0, 3) 
y= 2×2+5x3 
y=2(0)2+5(0)3=3  3 (or) (0, 3) 
Important Notes on yIntercept
 We substitute x=0 and solve for y to find the yintercept.
 In the same way, we substitute y=0 and solve for x to find the xintercept.
 The lines parallel to the yaxis cannot have yintercepts as they do not intersect the yaxis anywhere.
 The yintercept of a line is widely used as an initial point while graphing a line by plotting two points.
 A function has cannot have more than one yintercept.
☛ Related Topics:
Examples on Y Intercept

Example 1: Find the yintercept of the following functions using the formula to find the yintercept: a) y = x2 – 3x + 2 b) y = (x2 – 1) / x
Solution:
Using the yintercept formula, to find the yintercept of a function, we just substitute x = 0 in it and solve for y.
a) Substitute x = 0 in y = x2 – 3x + 2, we get
y = 02 – 3(0) + 2 = 2
So its yintercept = (0, y) = (0, 2)
b) Substitute x = 0 in y = (x2 – 1) / x, we get
y = (02 – 1) / 0 = 1/0 = Not defined
So the given function doesn’t have a yintercept.
Answer: a) (0, 2); b) Does Not Exist

Example 2: If the yintercept of a function y = a (x – 1) (x – 2) (x – 3) is (0, 12), then find the value of “a”.
Solution:
The equation of the given function is:
y = a (x – 1) (x – 2) (x – 3)
Using the yintercept formula, it can be obtained by substituting x = 0 in it.
y = a (0 – 1) (0 – 2) (0 – 3) = 6a
So the yintercept is (0, 6a)
But the problem says that the yintercept of the given function is (0, 12). Thus,
6a = 12
Dividing both sides by 6,
a = 2
Answer: a = 2

Example 3: If the yintercept of the function y = 3×2 + ax + b is (0, 5) then find the value of ‘b’.
Solution:
By using the y intercept formula the yintercept of the given function is obtained by substituting x = 0
i.e., the yintercept is, 3(0)2 + a (0) + b = b.
But it is given that the yintercept is, (0, 5) (or) 5.
So, b = 5.
Answer: b = 5.
Practice Questions on y Intercept
FAQs on y Intercept
What is the Meaning of Y Intercept?
The yintercept of a graph is a point where the graph cuts the yaxis. If the graph is a function, then it has a maximum of one yintercept.
What is the Slope and Y Intercept of y = 6?
Comparing y=6 with y=mx+b (pointslope form), we get,
 the slope, m = 0 and
 the yintercept, b=6
How do you Find the YIntercept on the Graphing Calculator?
We use the button “y=” on the calculator to enter the function and then press on the “graph”. Then the graph of the function is displayed on the screen. Then press on the “zoom” button. Then press on the “trace” button and enter 0. It will then show the value of y at which x is 0
What is Y Intercept Formula?
The yintercept formula is used to find the yintercept of a function. i.e., it is used to find the point where the graph of the function cuts the xaxis. The formula to find yintercept says that the yintercept of a function y = f(x) is substituting x = 0 in it and solving for y.
How to Derive Y Intercept Formula?
According to the definition of yintercept, the yintercept of a graph is the point where it cuts (or) intersects the yaxis. We know that on the yaxis the xcoordinate is 0. Hence the formula to find the yintercept of a function y = f(x) is just substituting x = 0 and solving for y.
What are the Applications of Y Intercept Formula?
The yintercept formula is used to find the yintercept of a function. The yintercept is mainly used in the process of graphing a function.
Find the Y Intercept of the Graph Represented by the Equation x = y2+2 y3.
To find the yintercept, we substitute x = 0 in the given equation and solve for y. Then,
y2+2y3 = 0
(y+3)(y1) = 0
y=3
yintercepts are (0, 3) and (0, 1)
How to Use the Y Intercept Formula in Finding the Y Intercept From a Graph?
The yintercept formula says that the yintercept of a function y = f(x) is obtained by substituting x = 0 in it. Using this, the yintercept of a graph is the point on the graph whose xcoordinate is 0. i.e., just look for the point where the graph intersects the yaxis and it is the yintercept.
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