Find the x -intercept and the y -intercept of the graph of each equation. Do not graph the equat

step 1 Given the equation 2x equals 3y minus 11, I want to determine what the x intercept and y interce

Find the x -intercept and the y -intercept of the graph of...

Key Concepts

linear equation

A linear equation represents a straight line when graphed in the coordinate plane. Understanding linear equations involves grasping how changes in the equation’s constants affect the line’s slope and intercepts. The intercepts are crucial components of a linear equation because they give immediate information about where the line interacts with the coordinate axes.

x-intercept

The x-intercept is the point at which a graph crosses the x-axis. At this point, the value of y is zero, so finding the x-intercept involves substituting y = 0 into the equation and solving for x. This concept is fundamental in understanding the behavior of linear graphs and other functions on a coordinate plane.

y-intercept

The y-intercept is where a graph crosses the y-axis. Here, the value of x is zero, and by substituting x = 0 into the equation, we can solve for y. This concept is key to graph analysis as it provides a starting point for plotting a line, and it offers insights into the function’s initial value in various applications.

substitution method

The substitution method is a basic algebraic technique used to find intercepts or solve systems of equations by replacing one variable with a known value. In the context of finding intercepts, substituting x = 0 or y = 0 simplifies the equation and allows for solving the corresponding variable, making it an essential tool in algebra.

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