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# Determine which of the following expressions displays a linear realtionship.use multiple representations to explain your reasoning?

a. square root of x
b.1/2
c. 3 + 0.5x
x + 7

### 1 Answer by Expert Tutors

Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
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Hi Travina;
A linear equation is in either of the following formats...
Standard format...Ax+By=C, A>0
Slope-intercept...y=mx+b, m is the slope, b is y-intercept, value of y when x=0.
Point-slope...(y-y1)=m(x-x1), m is the slope, and one coordinate on the line must be inputted to complete the equation.

An expression, which is what you are presenting, has no equal sign.  Henceforth, it cannot have linear qualities.  Nonetheless, I will assume that the four expressions are actually equations which =y.  Henceforth, we can apply the above.

a. square root of x
This can also be represented as x1/2, y=x1/2.  This is not linear.
b.1/2
This is not an expression because there is no variable.
c. 3 + 0.5x
As y=3+0.5x, this is in slope-intercept format...y=0.5x+3, y=mx+b.  Slope is 0.5.  The y-intercept is 3, corresponding to the point (0,3).
x + 7
As y=x+7, this is also in slope-intercept format...y=x+7, y=mx+b.  Slope is 1.  The y-intercept is 7, corresponding to the point (0,7).