Definition Of The Y Intercept

Y Intercept

The y-intercept is the signal where the graph intersects the y-axis. 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 role can have. They are the ten-intercept and the y-intercept. An intercept of a role is a point where the graph of the function cuts the centrality.

Let u.s.a. understand the significant of the y-intercept along with its formula and examples.

1.	What is Y-Intercept?
2.	Y-Intercept Formula
3.	Y-Intercept of a Direct Line
iv.	How To Find The Y-Intercept?
5.	Y-Intercept of a Quadratic Role (Parabola)
6.	FAQs on Y-Intercept

What is Y Intercept?

The y intercept of a graph is the point where the graph intersects the y-axis. Nosotros know that the x-coordinate of any point on the y-axis is 0. Then the x-coordinate of a y-intercept is 0.

y intercept definition

Here is an example of a y-intercept. Consider the line y = x+ three. This graph meets the y-axis at the point (0,iii). Thus (0,iii) is the y-intercept of the line y = x+ 3.

y intercept example

Y-Intercept Formula

The y-intercept of a office is a point where its graph would meet the y-axis. The ten-coordinate of any point on the y-centrality is 0 and we apply this fact to derive the formula to find the y-intercept. i.e., the y-intercept of a office is of the class (0, y). Thus, the formula to discover the y-intercept is:

y intercept formula

Y Intercept Formula

Here are the steps to find the y intercept of a function y = f(10),

we merely substitute x = 0 in it.
solve for y.
represent the y-intercept as the bespeak (0, y).

Here are some examples of y intercepts.

The y-intercept of y = 5xⁱⁱ + ii is, (0, ii) because when we substitute x = 0, we get y = 5(0)^two + 2 = ii.
The y-intercept of y = -5e^ten is (0, -v) because when nosotros substitute x = 0, nosotros get y = -5e⁰ = -5.

Y-Intercept of a Directly 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 acquire to detect the y intercept of a straight line represented in different forms.

Y-Intercept in Full general Form

The equation of a straight line in general form is ax+by+c=0. For y-intercept, nosotros substitute x=0 and solve information technology for y.

a(0)+ by + c =0

past + c =0

y = - c/b

Thus, the y-intercept of the equation of a line in general form is:(0, -c/b) or -c/b

y-Intercept in Slope-Intercept Form

The equation of the line in the slope-intercept form is, y=mx+b. Past the definition of the slope-intercept form itself, b is the y-intercept of the line. You try by substituting 10=0 in y=mx+b and meet whether yous go b as the y-intercept. Thus, the y-intercept of the equation of a line in the slope-intercept form is (0, b) or b.

y-Intercept in Point-Slope Form

The equation of the line in the point-gradient course is, y-y₁=m ten-x₁. For y-intercept, nosotros substitute ten=0 and solve it for y.

y-y₁ = m (0-ten₁ )

y-y₁= - mx₁

y = y₁ - mx₁

Thus, the y-intercept of the equation of a line in the betoken-slope form is: (0, y₁ - mx₁) or y₁ - mx₁

How To Notice Y-Intercept?

We have derived the formulas to detect the y-intercept of a line where the equation of the straight line is in different forms. In fact, we practise not need to utilise any of these formulas to find the y-intercept of a straight line. The y-intercept of the polynomial function of the form y = a₁xⁿ+ a_two 10^north-1+ ... + a_n is just its constant term a_{due north} (or) (0, a_n).

We merely substitute 10=0 in the equation of the line and solve for y. Then the corresponding y-intercept is y or (0, y).

Equation of Line	Substitute x=0 and solve for y	y intercept
3x+5y -vi=0	three(0)+5y-six =0 5y-6=0 y=6/5	vi/five (or) (0, 6/5)
y= 2x-3	y=2(0)-3=-3	-3 (or) (0, -iii)

Equation of Line

Substitute x=0 and solve for y

y intercept

3x+5y -vi=0

three(0)+5y-six =0

5y-6=0

y=6/5

vi/five (or) (0, 6/5)

y= 2x-3

y=2(0)-3=-3

-3 (or) (0, -iii)

The y-intercept of a function tin be hands constitute past graphing information technology using the graphing computer and locating the point where the graph cuts the y-axis. A function has only one y-intercept considering otherwise, it fails the vertical line examination. The y-intercept of the second equation of the table (y = 2x - iii) is shown in the graph below.

y intercept of a straight line

Y-Intercept of a Quadratic Function (Parabola)

The process for finding the y-intercept of a quadratic function or the y-intercept of a parabola is the same equally 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 x=0 and solve for y	y-Intercept
y= ten²-2x -3	y=0^two-ii(0)-three=-3	-iii (or) (0, -3)
y= 2x²+5x-three	y=2(0)^two+5(0)-3=-three	-iii (or) (0, -three)

y intercept of a parabola

Of import Notes on y-Intercept

We substitute x=0 and solve for y to detect the y-intercept.
In the same way, we substitute y=0 and solve for x to observe the x-intercept.
The lines parallel to the y-axis cannot have y-intercepts as they do not intersect the y-axis anywhere.
The y-intercept of a line is widely used every bit an initial point while graphing a line past plotting two points.
A function has cannot have more than 1 y-intercept.

☛ Related Topics:

Y-Intercept Reckoner
X-Intercept Formula
Ten-Intercept Reckoner

Examples on Y Intercept

Case i: Find the y-intercept of the following functions using the formula to find the y-intercept: a) y = xⁱⁱ - 3x + ii b) y = (xⁱⁱ - 1) / 10

Solution:

Using the y-intercept formula, to notice the y-intercept of a function, nosotros just substitute 10 = 0 in it and solve for y.

a) Substitute x = 0 in y = ten² - 3x + 2, we become

y = 0ⁱⁱ - three(0) + 2 = 2

Then its y-intercept = (0, y) = (0, 2)

b) Substitute 10 = 0 in y = (10ⁱⁱ - 1) / 10, nosotros get

y = (0² - 1) / 0 = -1/0 = Non defined

So the given office doesn't have a y-intercept.

Answer: a) (0, 2); b) Does Not Be
Example 2: If the y-intercept of a function y = a (ten - 1) (x - ii) (x - three) is (0, 12), then find the value of "a".

Solution:

The equation of the given function is:

y = a (x - 1) (x - 2) (x - iii)

Using the y-intercept formula, it can be obtained by substituting ten = 0 in it.

y = a (0 - one) (0 - two) (0 - 3) = -6a

So the y-intercept is (0, -6a)

But the problem says that the y-intercept of the given function is (0, 12). Thus,

-6a = 12

Dividing both sides by -6,

a = -2

Reply: a = -2
Case three: If the y-intercept of the role y = 3x² + ax + b is (0, -v) and so find the value of 'b'.

Solution:

By using the y intercept formula the y-intercept of the given function is obtained by substituting x = 0

i.east., the y-intercept is, 3(0)² + a (0) + b = b.

But it is given that the y-intercept is, (0, -v) (or) -5.

So, b = -5.

Respond: b = -v.

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Practise Questions on y Intercept

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FAQs on y Intercept

What is the Meaning of Y Intercept?

The y-intercept of a graph is a indicate where the graph cuts the y-axis. If the graph is a role, then it has a maximum of ane y-intercept.

What is the Slope and Y Intercept of y = half dozen?

Comparing y=6 with y=mx+b (point-slope class), we get,

the slope, m = 0 and
the y-intercept, b=6

How practice you lot Find the Y-Intercept on the Graphing Calculator?

We use the button "y=" on the figurer to enter the function and so press on the "graph". Then the graph of the role is displayed on the screen. And then printing on the "zoom" button. So printing on the "trace" button and enter 0. Information technology will then show the value of y at which x is 0

What is Y Intercept Formula?

The y-intercept formula is used to find the y-intercept of a office. i.e., information technology is used to find the point where the graph of the function cuts the ten-axis. The formula to detect y-intercept says that the y-intercept of a part y = f(10) is substituting 10 = 0 in it and solving for y.

How to Derive Y Intercept Formula?

According to the definition of y-intercept, the y-intercept of a graph is the point where it cuts (or) intersects the y-centrality. We know that on the y-centrality the x-coordinate is 0. Hence the formula to find the y-intercept of a function y = f(x) is merely substituting x = 0 and solving for y.

What are the Applications of Y Intercept Formula?

The y-intercept formula is used to find the y-intercept of a role. The y-intercept is mainly used in the process of graphing a function.

Notice the Y Intercept of the Graph Represented by the Equation 10 = y²+2 y-3.

To observe the y-intercept, nosotros substitute x = 0 in the given equation and solve for y. Then,

y^two+2y-iii = 0
(y+3)(y-i) = 0
y=-3

y-intercepts are (0, -3) and (0, 1)

How to Apply the Y Intercept Formula in Finding the Y Intercept From a Graph?

The y-intercept formula says that the y-intercept of a function y = f(x) is obtained by substituting x = 0 in it. Using this, the y-intercept of a graph is the point on the graph whose ten-coordinate is 0. i.e., simply wait for the point where the graph intersects the y-centrality and it is the y-intercept.