Question

(70 points)Which of the following has a graph that is a straight line?Equation 1: y = 5x2 + 41Equation 2: y = 14x5 − 4Equation 3: y = 12x + 17Equation 4: y4 = 2x − 1Which of the following ordered pairs could be placed in the table and still have the relation qualify as a linear function? Input(x)Output(y)1123956??(7, 3)(7, 10)(3, 3)(3, 10)

Answer 1

An equation of a line has the next general form:

`y=mx+b`

Then, from the given equations the one that has a graph that is a straight line is:

`y=12x+17`

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A linear function have a proportional relationship between its variables.

Then, you need to find the relation in the given data:

`\begin{gathered} (y_2-y_1)/(x_2-x_1) \\ \\ (9-12)/(3-1)=-(3)/(2) \\ \\ (6-9)/(5-3)=-(3)/(2) \end{gathered}`

The constant of proportionality is -3/2, then ordered pair that can be placed in the table needs to follow that constant:

`\begin{gathered} (7,3) \\ (3-6)/(7-5)=-(3)/(2) \end{gathered}`The point is (7,3)