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80 POINTS for right answer! 4 questions! Math only



Question 1 (Multiple Choice Worth 4 points)



(07.05A)


Which of the following has a graph that is a straight line?


Equation 1: y = 5x2 + 41


Equation 2: y = 14x5 − 4


Equation 3: y = 12x + 17


Equation 4: y4 = 2x − 1




Which 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)



−1 4

0 7

1 10

? ?



(2, 7)


(2, 13)


(1, 7)


(−1, 13)



Which statement best explains whether the table represents a linear or nonlinear function?




Input

(x)


Output

(y)



−2 7

−5 4

−8 1

−11 −2



It is a linear function because there is a constant rate of change in both the input and output values.


It is a nonlinear function because there is a constant rate of change in both the input and output values.


It is a linear function because the input values are decreasing.


It is a nonlinear function because the input values are increasing.



Which statement best explains whether y = 3x + 5 is a linear function or a nonlinear function?


It is a linear function because its graph contains the points (0, 0), (1, 0), (2, 8), which are on a straight line.


It is a linear function because its graph contains the points (0, 0), (1, 0), (2, 4), which are not on a straight line.


It is a nonlinear function because its graph contains the points (0, 5), (1, 8), (2, 11), which are on a straight line.


It is a linear function because its graph contains the points (0, 5), (1, 8), (2, 11), which are on a straight line.

Verified Answer :

dalendrk

1.
A graph of linear function is a straight line.
Linear function in a slope-intercept form: y = mx + b

Answer: Equation 3: y = 12x + 17.

2.
x|-1 | 0 | 1 | ? |
y| 4 | 7 |10| ? |

a slope: \(m=\dfrac{y_2-y_1}{x_2-x_1}\)

We choose:
\((-1; 4)\to x_1=-1\ and\ y_1=4\\(0;\ 7)\to x_2=0\ and\ y_2=7\)

subtitute:

\(m=\dfrac{7-4}{0-(-1)}=\dfrac{3}{1}=3\)

a slope-intercept form: \(y-y_1=m(x-x_1)\)

subtitute:

\(y-4=3(x-(-1))\\\\y-4=3(x+1)\\\\y-4=3x+3\ \ \ \ |add\ 4\ to\ both\ sides\\\\y=3x+7\ (*)\)

subtitute x = 2 to the equation (*):

\(y=3\cdot2+7=6+7=13\)

Answer: (2, 13)


3.
(-2; 7), (-5; 4)

the slope: \(m=\dfrac{4-7}{-5-(-2)}=\dfrac{-3}{-5+2}=\dfrac{-3}{-3}=1\)

\(y-7=1(x-(-2))\to y-7=x+2\ \ \ \ |add\ 7\ to\ both\ sides\\y=x+9\)

check other:

\((-8;\ 1)\to L=1;\ R=-8+9=1;\ L=R-correct\\(-11;-2)\to L=-2;\ R=-11+9=-2;\ L=R-correct\)

The conclusion: It's a linear function

Answer: It is a linear function because there is a constant rate of change in both the input and output values.


4.
y = 3x + 5    /look at the picture/

Answer: It is a linear function because its graph contains the points (0, 5), (1, 8), (2, 11), which are on a straight line.


check:
\((0; 5)\to L=5; R=3\cdot0+5=5;\ L=R-correct\\(1;\ 8)\to L=8;\ R=3\cdot1+5=8;\ L=R-correct\\(2;\ 11)\to L=11;\ R=3\cdot2+5=11;\ L=R-correct\)

View image dalendrk

Answer:it’s linear and is straight

Step-by-step explanation:

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