Question

coordinate planes
$y = -2x$
$y = 3x - 4$
$y = \frac{1}{2}x + 1$
$y = x - 3$

Explanation:

Step1: Calculate $y$ for $y=-2x$

Substitute $x$ values:
$x=-3$: $y=-2(-3)=6$
$x=-2$: $y=-2(-2)=4$
$x=0$: $y=-2(0)=0$
$x=1$: $y=-2(1)=-2$
$x=3$: $y=-2(3)=-6$

Step2: Calculate $y$ for $y=3x-4$

Substitute $x$ values:
$x=2$: $y=3(2)-4=2$
$x=3$: $y=3(3)-4=5$
$x=0$: $y=3(0)-4=-4$
$x=-1$: $y=3(-1)-4=-7$
$x=1$: $y=3(1)-4=-1$

Step3: Verify $y=\frac{1}{2}x+1$ values

Substitute $x$ values:
$x=-6$: $y=\frac{1}{2}(-6)+1=-2$
$x=-4$: $y=\frac{1}{2}(-4)+1=-1$
$x=-2$: $y=\frac{1}{2}(-2)+1=0$
$x=0$: $y=\frac{1}{2}(0)+1=1$
$x=2$: $y=\frac{1}{2}(2)+1=2$
$x=4$: $y=\frac{1}{2}(4)+1=3$
$x=6$: $y=\frac{1}{2}(6)+1=4$

Step4: Calculate $y$ for $y=x-3$

Substitute $x$ values:
$x=6$: $y=6-3=3$
$x=4$: $y=4-3=1$
$x=2$: $y=2-3=-1$
$x=0$: $y=0-3=-3$
$x=-1$: $y=-1-3=-4$
$x=-2$: $y=-2-3=-5$
$x=-3$: $y=-3-3=-6$

Answer:

For $y=-2x$:

$x$	$y$
$-2$	$4$
$0$	$0$
$1$	$-2$
$3$	$-6$

For $y=3x-4$:

$x$	$y$
$3$	$5$
$0$	$-4$
$-1$	$-7$
$1$	$-1$

For $y=\frac{1}{2}x+1$ (verified):

$x$	$y$
$-4$	$-1$
$-2$	$0$
$0$	$1$
$2$	$2$
$4$	$3$
$6$	$4$

For $y=x-3$:

$x$	$y$
$4$	$1$
$2$	$-1$
$0$	$-3$
$-1$	$-4$
$-2$	$-5$
$-3$	$-6$

(To graph each line, plot the $(x,y)$ points and draw a straight line through them)