Question

80 POINTS for right answer! 4 questions! Math only

Answer 1

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

Answer 2

1. Equation 3, there is a degree of 1
2. (2,13)
3. It is a linear function because there is a constant rate of change in both the input and output values. 
4. It is a linear function because its graph contains the points (0, 0), (1, 0), (2, 8), which are on a straight line.