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It is relatively easy to determine whether an equation is a function by solving for y. When you are given an equation and a specific value for x, there should only be one corresponding y-value for that x-value. For example, y = x + 1 is a function because y will always be one greater than x.
Given the graph of a line, you can determine the equation in two ways, using slope-intercept form, y=MX+b y = m x + b, or point-slope form, yy1= m(xx1) y y 1 = m (x × 1) . The slope and one point on the line is all that is needed to write the equation of a line.
The formula y = MX + b is said to be a linear function. That means the graph of this function will be a straight line on the (x, y) plane. Since we will be graphing (x, y) points, though, we will do our thinking with the 'y = MX + b' form for a while.
Given the graph of a line, you can determine the equation in two ways, using slope-intercept form, y=MX+b y = m x + b, or point-slope form, yy1= m(xx1) y y 1 = m (x × 1) . The slope and one point on the line is all that is needed to write the equation of a line.
Suggested clip Writing Linear Equations — MathHelp.com — Algebra Help — YouTubeYouTubeStart of suggested client of suggested clip Writing Linear Equations — MathHelp.com — Algebra Help — YouTube
Example: y = 2x + 1 is a linear equation: The graph of y = 2x+1 is a straight line. When x increases, y increases twice as fast, so we need 2x. When x is 0, y is already 1.
2:43 5:40 Suggested clip Determining if Something is a Function — YouTubeYouTubeStart of suggested client of suggested clip Determining if Something is a Function — YouTube
2:40 5:40 Suggested clip Determining if Something is a Function — YouTubeYouTubeStart of suggested client of suggested clip Determining if Something is a Function — YouTube
Determining whether a relation is a function involves making sure that for every input there is only one output. In order for a relation to be called a function, each X value must have exactly one Y value. X has to have exactly one Y value.
A function is a relation in which each input has only one output. In the relation, y is a function of x, because for each input x (1, 2, 3, or 0), there is only one output y. x is not a function of y, because the input y = 3 has multiple outputs: x = 1 and x = 2.
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