intercept

(noun)

the coordinate of the point at which a curve intersects an axis

Related Terms

Examples of intercept in the following topics:

  • Slope-Intercept Equations

    • One of the most common representations for a line is with the slope-intercept form.
    • Writing an equation in slope-intercept form is valuable since from the form it is easy to identify the slope and $y$-intercept.  
    • Let's write the equation $3x+2y=-4$ in slope-intercept form and identify the slope and $y$-intercept.
    • Now that the equation is in slope-intercept form, we see that the slope $m=-\frac{3}{2}$, and the $y$-intercept $b=-2$.
    • The slope is $2$, and the $y$-intercept is $-1$.  

  • Slope and Intercept

    • The concepts of slope and intercept are essential to understand in the context of graphing data.
    • If the curve in question is given as $y=f(x)$, the $y$-coordinate of the $y$-intercept is found by calculating $f(0)$.
    • Functions which are undefined at $x=0$ have no $y$-intercept.
    • Analogously, an $x$-intercept is a point where the graph of a function or relation intersects with the $x$-axis.
    • The zeros, or roots, of such a function or relation are the $x$-coordinates of these $x$-intercepts.

  • Solving Problems with Rational Functions

    • Rational functions can have zero, one, or multiple $x$-intercepts.
    • Find the $x$-intercepts of the function $f(x) = \frac{x^2 - 3x + 2}{x^2 - 2x -3}$.
    • The $x$-intercepts can thus be found at 1 and 2.
    • Thus, this function does not have any $x$-intercepts.
    • Thus there are three roots, or $x$-intercepts: $0$, $-\sqrt{2}$ and $\sqrt{2}$.

  • Parts of a Parabola

    • The y-intercept is the point at which the parabola crosses the y-axis.
    • The x-intercepts are the points at which the parabola crosses the x-axis.
    • There may be zero, one, or two $x$-intercepts.
    • These are the same roots that are observable as the $x$-intercepts of the parabola.
    • A parabola can have no x-intercepts, one x-intercept, or two x-intercepts.

  • Slope and Y-Intercept of a Linear Equation

    • For the linear equation y = a + bx, b = slope and a = y-intercept.
    • From algebra recall that the slope is a number that describes the steepness of a line and the y-intercept is
    • What is the y-intercept and what is the slope?
    • The y-intercept is 25 (a = 25).

  • Linear Equations in Standard Form

    • Any linear equation can be written in standard form, which makes it easy to calculate the zero, or $x$-intercept, of the equation.
    • For example, consider an equation in slope-intercept form: $y = -12x +5$.
    • We know that the y-intercept of a linear equation can easily be found by putting the equation in slope-intercept form.
    • However, the zero, or $x$-intercept of a linear equation can easily be found by putting it into standard form.
    • For a linear equation in standard form, if $A$ is nonzero, then the $x$-intercept occurs at $x = \frac{C}{A}$.

  • Slope and Intercept

    • In the regression line equation the constant $m$ is the slope of the line and $b$ is the $y$-intercept.
    • The constant $$$m$ is slope of the line and $b$ is the $y$-intercept -- the value where the line cross the $y$ axis.
    • An equation where y is the dependent variable, x is the independent variable, m is the slope, and b is the intercept.

  • The Equation of a Line

    • The intercept of the fitted line is such that it passes through the center of mass $(x, y)$ of the data points.
    • Where $m$ (slope) and $b$ (intercept) designate constants.
    • In this particular equation, the constant $m$ determines the slope or gradient of that line, and the constant term $b$ determines the point at which the line crosses the $y$-axis, otherwise known as the $y$-intercept.
    • Three lines — the red and blue lines have the same slope, while the red and green ones have same y-intercept.

  • Interpreting regression line parameter estimates

    • The slope and intercept estimates for the Elmhurst data are -0.0431 and 24.3.
    • (It would be reasonable to contact the college and ask if the relationship is causal, i.e. if Elmhurst College's aid decisions are partially based on students' family income. ) The estimated intercept b0 = 24.3 (in $1000s) describes the average aid if a student's family had no income.
    • The meaning of the intercept is relevant to this application since the family income for some students at Elmhurst is $0.
    • In other applications, the intercept may have little or no practical value if there are no observations where x is near zero.
    • The intercept describes the average outcome of y if x = 0 and the linear model is valid all the way to x = 0, which in many applications is not the case.

  • What is a Linear Function?

    • Linear functions are algebraic equations whose graphs are straight lines with unique values for their slope and y-intercepts.
    • For example, a common equation, $y=mx+b$, (namely the slope-intercept form, which we will learn more about later) is a linear function because it meets both criteria with $x$ and $y$ as variables and $m$ and $b$ as constants.  
    • In the linear function graphs below, the constant, $m$, determines the slope or gradient of that line, and the constant term, $b$, determines the point at which the line crosses the $y$-axis, otherwise known as the $y$-intercept.
    • Horizontal lines have a slope of zero and is represented by the form, $y=b$, where $b$ is the $y$-intercept.  
    • The blue line has a positive slope of $\frac{1}{2}$ and a $y$-intercept of $-3$; the red line has a negative slope of $-1$ and a $y$-intercept of $5$.