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We’re not sure when or why this term was coined, but it’s a common one. It usually refers to a point in a function where the graph changes from going up to going down. But for inbound marketers, a marketing plan can also be viewed as a graph in which inbound marketing effectiveness measures how high the inbound marketing ROI climbs up the curve before turning around and coming back down.
The notion may be extended for 3-dimensional space and higher dimensions, as well as for other coordinate axes, possibly with other names. For example, one may speak of the I-intercept of the current–voltage characteristic of, say, a diode. (In electrical engineering, I is the symbol used for electric current.)
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) finding the intercepts is really important. There are two types 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 cuts the axis. Let us understand the meaning of y-intercept and the calculation of y-intercept using the y-intercept formula with a few examples. (Source: www.cuemath.com)
Example 1: Find the y-intercept of the following functions using the formula to find the y-intercept: a) y = x
Example: Consider a graph containing the points (3, 6) and (-1, -2). Find the y-intercept
Just like the slope of a line, many algebra classes go over the y-intercept of a line without explaining how to use it in the real world. The y-intercept of a line is the value of \(y\) where the line crosses the y-axis. In other words, it is the value of \(y\) when the value of \(x\) is equal to 0. Sometimes this has true meaning for the model that the line provides, but other times it is meaningless. We will encounter examples of both types in this section.
I use the example below in my post about how to interpret regression p-values and coefficients. The graph displays a regression model that assesses the relationship between height and weight. For this post, I modified the y-axis scale to illustrate the y-intercept, but the overall results haven’t changed. (Source: statisticsbyjim.com)
In this lesson, we learn how to graph our line using the y-intercept and the slope. First, we know that the y-intercept (b) is on the y-axis, so we graph that point. Next, we use the slope to find a second point in relation to that intercept. The following video will show you how this is done with two examples.
Khan Academy: Slope-intercept Examples (03:45 mins, Transcript)
Find the y-intercept of a linear function using the slope and a given point (
First, identify the slope and a point on the graph. Once this is done, write a linear equation in slope-intercept form (y = mx + b). Using the given point (x, y) and the slope m, rewrite the equation by substituting the appropriate values for x, y, and m. Given this information, solve the equation for b to identify the y-intercept.)