The x-intercept of a line is the point where the line crosses the x-axis, indicating the value of x when the value of y is zero. This point provides important information about the behavior and characteristics of the line.
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The x-intercept of a line is the value of $x$ where the line crosses the $x$-axis, or where $y = 0$.
To find the $x$-intercept, you can set $y = 0$ in the equation of the line and solve for $x$.
The $x$-intercept is an important feature when graphing lines, as it provides information about the behavior of the line.
In the slope-intercept form of a linear equation, $y = mx + b$, the $x$-intercept is given by $x = -b/m$.
When solving systems of equations by graphing, the $x$-intercepts of the lines are used to find the point of intersection, which is the solution to the system.
Review Questions
Explain how to find the x-intercept of a line given its equation in slope-intercept form.
To find the $x$-intercept of a line given in slope-intercept form, $y = mx + b$, you set $y = 0$ and solve for $x$. This gives you the $x$-value where the line crosses the $x$-axis, which is $x = -b/m$. The $x$-intercept provides important information about the behavior of the line, such as where it intersects the horizontal axis.
Describe the role of the x-intercept when solving systems of equations by graphing.
When solving systems of equations by graphing, the $x$-intercepts of the lines are used to find the point of intersection, which is the solution to the system. The $x$-intercepts represent the values of $x$ where each line crosses the $x$-axis, and the point where the two lines intersect is the solution that satisfies both equations in the system.
Analyze how the x-intercept is related to the other key features of a line, such as the slope and y-intercept.
The $x$-intercept, slope, and $y$-intercept of a line are all interconnected. In the slope-intercept form, $y = mx + b$, the $x$-intercept is given by $x = -b/m$, which shows how it is related to both the slope ($m$) and the $y$-intercept ($b$). The $x$-intercept provides information about the horizontal positioning of the line, while the slope and $y$-intercept describe its orientation and vertical positioning, respectively. Understanding these relationships is crucial for analyzing and interpreting the characteristics of a line.