# Is a straight line a function

## Does a vertical line represent a function?

The origin of the name “linear” comes from the fact that the set of solutions of such an equation forms a straight line in the plane. In the linear function graphs.

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Linear Functions: Slope-Intercept Form. This form of a linear equation is often called slope-intercept form. A typical graph of one of these functions looks like this:. The slope is calculated from knowing any two distinct points on the line, x 1 , y 1 and x 2 , y 2. If the points are distinct, then the x coordinates cannot be the same and so zeros in the denominator are avoided. The y-intercept can be calculated from any point if the slope is known. Since for any point x 1 , y 1.

In mathematics, the vertical line test is a visual way to determine if a curve is a graph of a function or not. A function can only have one output, y , for each unique input, x. If a vertical line intersects a curve on an xy -plane more than once then for one value of x the curve has more than one value of y , and so, the curve does not represent a function. If all vertical lines intersect a curve at most once then the curve represents a function. To use the vertical line test, take a ruler or other straight edge and draw a line parallel to the y -axis for any chosen value of x.

If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Math Algebra I Functions Recognizing functions. Recognizing functions from graph. Does a vertical line represent a function?

A linear function takes a number x as input and returns the number m x + b as This is called the equation of a straight line because if we plot the points that.
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Linear functions are algebraic equations whose graphs are straight lines with unique values for their slope and y-intercepts. A linear function is an algebraic equation in which each term is either a constant or the product of a constant and the first power of a single variable. Also, its graph is a straight line. Vertical lines are NOT functions, however, since each input is related to more than one output. Horizontal lines ARE functions because the relation set of points has the characteristic that each input is related to exactly one output.

In the applet below, lines can be dragged as a whole or with one of the two defining points. When a line is dragged or clicked upon, one of its equations is displayed just beneath the graph. With the Reduce box checked, the equation appears in its simplest form. The applet can display several lines simultaneously. To obtain additional lines, check the Duplicate box and start dragging one of the already present lines to the desired position.

Sketching the graph. The slope-intercept form. We will find that the graph of each degree leaves its characteristic signature on the x - y -plane. The graph of a first degree polynomial is always a straight line. The graph of a second degree polynomial is a curve known as a parabola.

## Linear Functions

A linear function is a function whose graph is a straight line. The line can't be vertical, since then we wouldn't have a function, but any other sort of straight line is fine. Now, are you ready to make the word "slope" a part of your life?

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