The y-intercept is the point where the graph intersects the y-axis. To graph, any function that is of the form y = f(x) seeing the intercepts is really important. There are two kinds of intercepts that a function can have. They are the x-intercept and the y-intercept.

An intercept of a function is a point where the graph of the function trims the axis. Let us understand the significance of the y-intercept along with its formula and examples.

What is Y Intercept?

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

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

Y-Intercept Formula

The y-intercept of a function is a point where its graph would encounter the y-axis. The x-coordinate of any point on the y-axis is 0 and we use this point to derive the formula to find the y-intercept. i.e., the y-intercept of a function is of the form (0, y). Thus, the formula to find the y-intercept is:

Y Intercept Formula

Here are the phases to find the y intercept of a function y = f(x),

• we just substitute x = 0 in it.
• solve for y.
• represent the y-intercept as the point (0, y).

Here are some examples of y-intercepts.

• The y-intercept of y = 5x² + 2 is, (0, 2) because when we substitute x = 0, we get y = 5(0)² + 2 = 2.
• The y-intercept of y = -5e^x is (0, -5) because when we substitute x = 0, we get y = -5e⁰ = -5.

Y-Intercept 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.

Y-Intercept in General Form

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

a(0)+ by + c =0

by + c =0

y = – c/b

Therefore, 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. By the meaningcof the slope-intercept form itself, b is the y-intercept of the line. You try by substituting x=0 in y=mx+b and notice 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 Form

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 Find Y-Intercept?

We have emanated the formulas to find the y-intercept of a line where the equation of the straight line is in different forms. In fact, we do not require to apply 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 + a₂ x^n-1+ … + a_n is just its constant term a_n (or) (0, a_n).

Important Notes on y-Intercept

• We substitute x=0 and solve for y to find the y-intercept.
• In the same way, we substitute y=0 and solve for x to find 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 as an initial point while graphing a line by plotting two points.
• A function has cannot have more than one y-intercept.

FAQs

Q: What is the Meaning of Y Intercept?

A: 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.

Q: What are the Slope and Y Intercept of y = 6?

A: Comparing y=6 with y=mx+b (point-slope form), we see,

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

Q: How do you See the Y-Intercept on the Graphing Calculator?

A: We use the button “y=” on the calculator to put the function and then press on the “graph”. Then the graph of the function is shown on the screen. Then press on the “zoom” button. Then hit on the “trace” button and enter 0. It will then display the value of y at which x is 0

Q: What is Y Intercept Formula?

A: The y-intercept formula is utilized to find the y-intercept of a function. i.e., it is used to see the point where the graph of the function cuts the x-axis. The formula to see y-intercept says that the y-intercept of a function y = f(x) is substituting x = 0 in it and solving for y.

Q: How to Derive Y Intercept Formula?

A: According to the description of y-intercept, the y-intercept of a graph is the point where it cuts (or) intersects the y-axis. We know that on the y-axis the x-coordinate is 0. Hence the formula to see the y-intercept of a function y = f(x) is just substituting x = 0 and solving for y.

Q: How to Utilize the Y Intercept Formula in Finding the Y Intercept From a Graph?

A: The y-intercept formula states that the y-intercept of a function y = f(x) is obtained by substituting x = 0 in it. Utilizing this, the y-intercept of a graph is the point on the graph whose x-coordinate is 0. i.e., just look for the point where the graph crosses the y-axis and it is the y-intercept.

Q: What are the Applications of Y Intercept Formula?

A: The y-intercept formula is utilized to find the y-intercept of a function. The y-intercept is mainly utilized in the process of graphing a function.