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):
, 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.
, 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.
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.
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.
is NOT a linear function, because y is linked to x in a <u>nonlinear way</u>, specifically, y is linked to the squared root of x, which means that is linked to , then x has not power equal to one in this case.
Not entirely sure, but it seem the answer could be B.) It will not be spread out vertically across the entire coordinate plane because in step 5, Nancy selected an incorrect scale on the y-axis.
, 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.
, 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.
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.
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.
is NOT a linear function, because y is linked to x in a <u>nonlinear way</u>, specifically, y is linked to the squared root of x, which means that is linked to
, then x has not power equal to one in this case.