Question

Pls help
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Answer 1

• Linear functions can be represented by a straight line, with an intercept and a constant slope. They are formed by a dependent varible (y) and an independent varible (x) whose power equals one, which means that y is related to x in a linear way (they have both power equal to one).
• The general equation of a linear function can be written as follows: y= a + b x, with a equal to a constant known as the intercept, and b equal to the slope.
• We can rewrite the equations you have attached as follow, by rearranging terms in order to clear y as a function of x (in order):

1. 
   `y=-19+(1)/(2)x`, is a linear function: y is linked to x in a linear way, the curve has the form y= a + b x, where a=-19 and b=1/2.
2. 
   `y=(1)/(3) x^(2)`, it is NOT a linear function, because y is linked to x in a way that is not linear (the power of x is different from zero, in this case the power of x equals 2 ), and the graph of this expression would not be linear.
3. 
   `y=(1)/(39)x +(5)/(13)` is a linear function: y is linked to x in a linear way (the power of x equals one), the curve in this case has the form y= a + b x, where a=1/39 and b=5/13.
4. 
   `y=x+(25)/(5)` is a linear function: y is linked to x in a linear way (the power of x equals one), and the curve has the form y= a + b x, where a=25/5 and b=1.
5. 
   `y=\sqrt[3]{x}` is NOT a linear function, because y is linked to x in a nonlinear way, specifically, y is linked to the squared root of x, which means that is linked to
   `x^{(1)/(3) }`, then x has not power equal to one in this case.