determing whether the equqtion defines

Mathematics
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Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b.

Jul 24th, 2014

A common form of a linear equation in the two variables x and y is

where m and b designate constants. 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 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.
Since terms of linear equations cannot contain products of distinct or equal variables, nor any power (other than 1) or other function of a variable, equations involving terms such as xy, x2, y1/3, and sin(x) are nonlinear

from 8x=5y+9 ==> 5y = 8x-9

==> y = (8/5)x-9/5 ans

second one,

x = 3y-9 ==> 3y = x+9 ==> y = (x/3)+ 3 ans

Jul 24th, 2014

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