Question

keep change change x ) x

first table (left top):

x	y =
-1	-4/5
-2	-1 2/5
-3	-2
-4	(blank)

(handwritten notes: -1, 3/5 next to some rows)

second table (middle top):

x	y =
-7	3
-9	(blank)
(blank)	6
(blank)	7,5

third table (right top):

x	y =
-1	-8
0	-9
1	-10
2	-11

handwritten: y = (3/5)x - 1/5, \take right devise by left\ (possibly typo)

fourth table (left bottom):

x	y =
(blank)	-5,2
-4	-5
0	-4,8
4	(blank)

fifth table (middle bottom):

x	y =
-5	6
-3	9
-1	(blank)
1	(blank)

sixth table (right bottom):

x	y =
(blank)	(blank)
(blank)	(blank)
(blank)	(blank)
(blank)	(blank)
(blank)	(blank)

Explanation:

Step1: Solve first table (use $y=\frac{3}{5}x-\frac{1}{5}$)

For $x=-4$:

$$\begin{align*} y&=\frac{3}{5}(-4)-\frac{1}{5}\\ &=\frac{-12 -1}{5}\\ &=-\frac{13}{5}=-2\frac{3}{5} \end{align*}$$

For $x=-2$ (verify):

$$\begin{align*} y&=\frac{3}{5}(-2)-\frac{1}{5}\\ &=\frac{-6-1}{5}=-\frac{7}{5}=-1\frac{2}{5} \ (\text{matches given}) \end{align*}$$

Step2: Solve second table (find slope first)

Slope $m=\frac{3-1.5}{-7-(-5)}=\frac{1.5}{-2}=-0.75=-\frac{3}{4}$
Equation: $y-1.5=-\frac{3}{4}(x+5)$ → $y=-\frac{3}{4}x-\frac{15}{4}+\frac{3}{2}=-\frac{3}{4}x-\frac{9}{4}$

For $x=-9$:

$y=-\frac{3}{4}(-9)-\frac{9}{4}=\frac{27-9}{4}=\frac{18}{4}=4.5$

For $y=6$:

$6=-\frac{3}{4}x-\frac{9}{4}$ → $24=-3x-9$ → $3x=-33$ → $x=-11$

For $y=7.5$:

$7.5=-\frac{3}{4}x-\frac{9}{4}$ → $30=-3x-9$ → $3x=-39$ → $x=-13$

Step3: Solve third table (find equation)

Slope $m=\frac{-8-(-7)}{-1-(-2)}=-1$
Equation: $y+7=-1(x+2)$ → $y=-x-9$
(Verifies with given values: $x=0,y=-9$; $x=1,y=-10$)

Step4: Solve fourth table (find equation)

Slope $m=\frac{-5.2-(-5.4)}{x_2-x_1}$. Use $x=-4,y=-5$ and $x=0,y=-4.8$:
$m=\frac{-4.8-(-5)}{0-(-4)}=\frac{0.2}{4}=0.05=\frac{1}{20}$
Equation: $y+5=\frac{1}{20}(x+4)$ → $y=\frac{1}{20}x+\frac{4}{20}-5=\frac{1}{20}x-4.8$

For $y=-5.4$:

$-5.4=\frac{1}{20}x-4.8$ → $\frac{1}{20}x=-0.6$ → $x=-12$

For $y=-5.2$:

$-5.2=\frac{1}{20}x-4.8$ → $\frac{1}{20}x=-0.4$ → $x=-8$

For $x=4$:

$y=\frac{1}{20}(4)-4.8=0.2-4.8=-4.6$

Step5: Solve fifth table (find equation)

Slope $m=\frac{6-3}{-5-(-7)}=\frac{3}{2}=1.5$
Equation: $y-3=1.5(x+7)$ → $y=1.5x+10.5+3=1.5x+13.5$

For $x=-1$:

$y=1.5(-1)+13.5=12$

For $x=1$:

$y=1.5(1)+13.5=15$

Step6: Sixth table (choose linear example, e.g., $y=2x+1$)

For $x=-2$: $y=2(-2)+1=-3$

For $x=-1$: $y=2(-1)+1=-1$

For $x=0$: $y=2(0)+1=1$

For $x=1$: $y=2(1)+1=3$

For $x=2$: $y=2(2)+1=5$

Answer:

First Table (x=-4): $\boldsymbol{-\frac{13}{5}=-2\frac{3}{5}}$

Second Table:

• x=-9: $\boldsymbol{4.5}$
• y=6: $\boldsymbol{x=-11}$
• y=7.5: $\boldsymbol{x=-13}$

Third Table Equation: $\boldsymbol{y=-x-9}$

Fourth Table:

• y=-5.4: $\boldsymbol{x=-12}$
• y=-5.2: $\boldsymbol{x=-8}$
• x=4: $\boldsymbol{y=-4.6}$

Fifth Table:

• x=-1: $\boldsymbol{y=12}$
• x=1: $\boldsymbol{y=15}$

Sixth Table (example linear fill):

x	y=
-1	-1
0	1
1	3
2	5