Finding Y-intercepts is not as complicated as it looks, intercepts are simple in themselves. They are simple points where the graph of the equation crosses the Y-axis or where the value of x=o. In this article, learn how to find the y-intercept or vertical intercept of a function and graphs in detail with examples
When finding the Y-Intercept of a graph or table you look for the point of intersection between the equation and the Y-axis. For a straight line, it occurs only once but for a graph it does not have a straight line, there can be different y-intercepts in the same graph.
The vertical intercept is the same as the Y-intercept because most graphs and equations set Y as the vertical line on the graph. On an (x,y) coordinate graph the x coordinates from the horizontal and y coordinates from the vertical line, where a line between the coordinates crossing the vertical line is Y intercept.
There is up to one way to find the y-intercept but it depends on your starting information. There are three ways below to determine the y-intercept on a graph, in a table, or with an equation.
Table of Contents
Finding Y intercept Using Slope and a Given Point
First of all, identify the slope and a point on a graph, then write a linear equation in slope-intercept form (y=mx+b). Now rewrite the equation using given points (x, y) by replacing the suitable values for x, y, and m. for example,
Just consider that a graph contains the point (-3, 5) where the slope is equal to 3.
Write a linear equation in slope-intercept form like that,
Y = mx + b
Now, substitute the corresponding value of the variables,
5 = (3)(-3) + b
Solve one-step equation from here,
5 = -9 + b
5 + 9 = b
14 = b
So, the y-intercept is 14.
Finding Y-intercept Using two Points from a Table or Graph
First of all, determine two coordinates (x, y) using a table or a graph and find the rise and run to identify the slope. Now find the difference in y-coordinates of the two points and calculate the rise. Then find the difference in the x-coordinates of the same two points and calculate the run. Now find the slope by dividing the difference of y-coordinates by the difference of x-coordinates, then solve the equation from the above method.
For example, a graph consists of two points (2, 4) and (-2, -4) to find the value of b.
Calculate the rise and run to find the slope which is 2.
rise/run = 4-(-4)/ 2-(-2) = 8/4 = 2
Now, write the equation in slope-intercept form, similar to the above method.
Y = mx + b
4 = (2)(2) + b
4 = 4 + b
4 – 4 = b
0 = b
Hence, b = 0, and the y-intercept is 0.
Finding y-intercept Using an Equation
When you already have an equation of the line, you should solve it algebraically to find the y intercept that already has a corresponding x-value of 0, substitute x with 0, and solve the equation.
For example the equation of the line is 4x + (-5y) = 10
By replacing the value of x.
4(0) + (-5y) = 10
0 – 5y = 10
Y = 10/-5
Y = -2
So, the y intercept is -2 of the line equation.
Finding Y-intercept in Quadratic Function
Finding the y-intercept of a quadratic function or parabola is the same as that of a line, where the parabola crosses the y-axis. We can write the standard form of a quadratic function as
Y = ax2 + bx + c, where x & y are variables and a, b, c are constants. Find y intercept by replacing 0 as the value of x as given below.
For example, the quadratic equation is y = 4x2 + 2x +2
Y = 4x2 + 2x + 2
Y = 4(0) + 2(0) + 2
Y = 0 + 0 + 2
Y = 2
So the y-intercept is 2 of the quadratic equation.