Question

table of values *plot on graph #1
first table: x values -1, 0, 1, 2; y = -2x + 3 (some cells empty)
second table: x values -2, -1, 0, 1; y = (2/5)x + 1 (cells empty)
third table: x values 1, 2, 3, 4; y values 7, 11, 15, 19; y = (equation partially visible)

Explanation:

Step1: Calculate $Y=-2x+3$ for each $x$

For $x=-1$: $Y=-2(-1)+3=2+3=5$
For $x=0$: $Y=-2(0)+3=0+3=3$
For $x=1$: $Y=-2(1)+3=-2+3=1$
For $x=2$: $Y=-2(2)+3=-4+3=-1$

Step2: Calculate $Y=\frac{2}{5}x+1$ for each $x$

For $x=-2$: $Y=\frac{2}{5}(-2)+1=-\frac{4}{5}+1=\frac{1}{5}=0.2$
For $x=-1$: $Y=\frac{2}{5}(-1)+1=-\frac{2}{5}+1=\frac{3}{5}=0.6$
For $x=0$: $Y=\frac{2}{5}(0)+1=0+1=1$
For $x=1$: $Y=\frac{2}{5}(1)+1=\frac{2}{5}+1=\frac{7}{5}=1.4$

Step3: Find equation for $y$ from $x,y$ pairs

Let $y=mx+b$. Use $x=1,y=7$: $7=m(1)+b$; $x=2,y=11$: $11=m(2)+b$
Subtract first equation: $11-7=2m+b-(m+b) \implies 4=m$
Substitute $m=4$: $7=4(1)+b \implies b=3$. So $y=4x+3$
Verify: $x=3$: $4(3)+3=15$; $x=4$: $4(4)+3=19$ (matches given values)

Answer:

1. Table for $Y=-2x+3$:

$x$	$Y$
0	3
1	1
2	-1

1. Table for $Y=\frac{2}{5}x+1$:

$x$	$Y$
-1	$0.6$
0	1
1	$1.4$

1. Equation for the third table: $y=4x+3$