Understanding the y-intercept: Definition, Equation Approach, and Graphical Approach

Y-intercept

The y-intercept is a term used in mathematics to refer to the point where a graph intersects or crosses the y-axis

The y-intercept is a term used in mathematics to refer to the point where a graph intersects or crosses the y-axis. This point represents the value of the dependent variable (usually denoted as y) when the independent variable (usually denoted as x) is equal to zero.

To find the y-intercept, you need to look at the equation of the graph or function. If the equation is in the form of y = mx + b, where m represents the slope and b represents the y-intercept, then the value of b is the y-intercept. This means that the y-intercept is the point (0, b) on the graph.

For example, let’s consider the equation of a straight line: y = 2x + 3. In this case, the coefficient of x is 2, which represents the slope of the line. The constant term 3 represents the y-intercept. So, the y-intercept is the point (0, 3) on the graph.

Another way to find the y-intercept is by observing the graph itself. Look for the point where the graph crosses the y-axis. This point will have an x-coordinate of 0, indicating that it lies entirely on the y-axis. The y-coordinate of this point gives you the value of the y-intercept.

To summarize, the y-intercept is the point where the graph of a function crosses the y-axis. It is found either by examining the equation of the graph or by observing where the graph intersects the y-axis, by looking for the point with an x-coordinate of 0.

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