What Does The Y Mean

Y Intercept

The y-intercept is the point where the graph intersects the y-centrality. To graph, any function that is of the grade y = f(10) finding the intercepts is actually important. There are two types of intercepts that a function can accept. They are the x-intercept and the y-intercept. An intercept of a part is a point where the graph of the function cuts the centrality.

Let us understand the meaning of the y-intercept along with its formula and examples.

i.	What is Y-Intercept?
2.	Y-Intercept Formula
3.	Y-Intercept of a Straight Line
iv.	How To Find The Y-Intercept?
5.	Y-Intercept of a Quadratic Office (Parabola)
six.	FAQs on Y-Intercept

What is Y Intercept?

The y intercept of a graph is the signal where the graph intersects the y-axis. We know that the x-coordinate of any point on the y-axis is 0. So the 10-coordinate of a y-intercept is 0.

y intercept definition

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

y intercept example

Y-Intercept Formula

The y-intercept of a function is a point where its graph would run into the y-axis. The x-coordinate of any point on the y-axis is 0 and we utilise this fact to derive the formula to observe the y-intercept. i.east., the y-intercept of a function is of the class (0, y). Thus, the formula to observe the y-intercept is:

y intercept formula

Y Intercept Formula

Hither are the steps to find the y intercept of a function y = f(x),

we just substitute x = 0 in information technology.
solve for y.
represent the y-intercept as the betoken (0, y).

Here are some examples of y intercepts.

The y-intercept of y = 5xⁱⁱ + two is, (0, 2) considering when we substitute ten = 0, we get y = 5(0)^two + 2 = 2.
The y-intercept of y = -5e¹⁰ is (0, -five) because when nosotros substitute x = 0, nosotros get y = -5e⁰ = -5.

Y-Intercept of a Direct 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. Allow us learn to find the y intercept of a direct line represented in unlike forms.

Y-Intercept in General Class

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

a(0)+ by + c =0

by + 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 Course

The equation of the line in the slope-intercept form is, y=mx+b. By the definition of the slope-intercept form itself, b is the y-intercept of the line. Yous try past substituting x=0 in y=mx+b and meet whether you get 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 Course

The equation of the line in the point-slope form is, y-y₁=m x-x₁. For y-intercept, we substitute x=0 and solve it for y.

y-y₁ = m (0-x₁ )

y-y₁= - mx₁

y = y₁ - mx₁

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

How To Detect Y-Intercept?

We take derived the formulas to detect the y-intercept of a line where the equation of the straight line is in unlike forms. In fact, we do not need to use any of these formulas to find the y-intercept of a direct line. The y-intercept of the polynomial function of the grade y = a₁tenⁿ+ a_two x^n-i+ ... + a_n is just its constant term a_n (or) (0, a_n).

Nosotros just substitute x=0 in the equation of the line and solve for y. And 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-6 =0 5y-half dozen=0 y=half-dozen/5	6/five (or) (0, 6/5)
y= 2x-3	y=2(0)-3=-iii	-3 (or) (0, -3)

Equation of Line

Substitute x=0 and solve for y

y intercept

3x+5y -vi=0

three(0)+5y-6 =0

5y-half dozen=0

y=half-dozen/5

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

y= 2x-3

y=2(0)-3=-iii

-3 (or) (0, -3)

The y-intercept of a function can exist easily found by graphing it using the graphing calculator and locating the point where the graph cuts the y-centrality. A part has merely one y-intercept considering otherwise, it fails the vertical line test. The y-intercept of the 2nd 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 procedure for finding the y-intercept of a quadratic function or the y-intercept of a parabola is the aforementioned as that of a line (as discussed in the previous section). If a quadratic equation is given, substitute ten = 0 and solve for y to go the y intercept.

Examples

Equation of Parabola	Substitute x=0 and solve for y	y-Intercept
y= 10²-2x -3	y=0^two-2(0)-iii=-3	-iii (or) (0, -3)
y= 2xⁱⁱ+5x-3	y=ii(0)²+5(0)-3=-3	-3 (or) (0, -3)

y intercept of a parabola

Important Notes on y-Intercept

We substitute x=0 and solve for y to discover the y-intercept.
In the same mode, we substitute y=0 and solve for x to detect the x-intercept.
The lines parallel to the y-centrality cannot have y-intercepts as they practise non intersect the y-axis anywhere.
The y-intercept of a line is widely used as an initial bespeak while graphing a line past plotting two points.
A role has cannot have more than one y-intercept.

☛ Related Topics:

Y-Intercept Calculator
10-Intercept Formula
Ten-Intercept Figurer

Examples on Y Intercept

Example one: Find the y-intercept of the post-obit functions using the formula to find the y-intercept: a) y = x² - 3x + two b) y = (x² - 1) / x

Solution:

Using the y-intercept formula, to observe the y-intercept of a function, nosotros just substitute x = 0 in information technology and solve for y.

a) Substitute x = 0 in y = x² - 3x + 2, we get

y = 0² - three(0) + 2 = 2

So its y-intercept = (0, y) = (0, ii)

b) Substitute x = 0 in y = (ten² - 1) / 10, we become

y = (0² - 1) / 0 = -1/0 = Non divers

And then the given function doesn't have a y-intercept.

Answer: a) (0, 2); b) Does Non Be
Case two: If the y-intercept of a function y = a (ten - 1) (x - 2) (10 - three) is (0, 12), and then find the value of "a".

Solution:

The equation of the given function is:

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

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

y = a (0 - one) (0 - 2) (0 - 3) = -6a

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

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

-6a = 12

Dividing both sides by -6,

a = -two

Reply: a = -2
Case 3: If the y-intercept of the function y = 3xⁱⁱ + ax + b is (0, -5) 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 ten = 0

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

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

So, b = -5.

Answer: b = -5.

become to slidego to slidego to slide

Keen learning in high school using simple cues

Indulging in rote learning, you are probable to forget concepts. With Cuemath, you lot will learn visually and be surprised by the outcomes.

Volume a Free Trial Form

Exercise Questions on y Intercept

go to slidego to slide

FAQs on y Intercept

What is the Meaning of Y Intercept?

The y-intercept of a graph is a point where the graph cuts the y-axis. If the graph is a function, then it has a maximum of one y-intercept.

What is the Slope and Y Intercept of y = vi?

Comparing y=vi with y=mx+b (point-gradient course), we get,

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

How do yous Find the Y-Intercept on the Graphing Reckoner?

Nosotros utilise the push "y=" on the computer to enter the part and then press on the "graph". Then the graph of the function is displayed on the screen. Then press on the "zoom" push. So press on the "trace" push and enter 0. Information technology will then testify the value of y at which x is 0

What is Y Intercept Formula?

The y-intercept formula is used to notice the y-intercept of a function. i.e., information technology is used to find the bespeak where the graph of the part cuts the x-axis. The formula to detect y-intercept says that the y-intercept of a function y = f(x) is substituting x = 0 in information technology 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 indicate where it cuts (or) intersects the y-centrality. Nosotros know that on the y-axis the x-coordinate is 0. Hence the formula to notice the y-intercept of a office y = f(ten) is just 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 function. The y-intercept is mainly used in the process of graphing a part.

Detect the Y Intercept of the Graph Represented by the Equation x = y²+2 y-three.

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

y²+2y-3 = 0
(y+3)(y-i) = 0
y=-3

y-intercepts are (0, -iii) and (0, ane)

How to Use 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 x-coordinate is 0. i.due east., just look for the betoken where the graph intersects the y-centrality and it is the y-intercept.