Question

name
date
math challenge solve and graph each equat
what gets smaller when you put more stuff in it? a hole!
complete the activity
$y = x - 4$
$y = 2x + 1$
$4x - 8 = y$
$y = x + 1$

Explanation:

Step1: Calculate y for $y=x-4$

For $x=-1$: $y=-1-4=-5$
For $x=0$: $y=0-4=-4$
For $x=1$: $y=1-4=-3$
For $x=2$: $y=2-4=-2$
For $x=3$: $y=3-4=-1$

Step2: Calculate y for $y=2x+1$

For $x=-3$: $y=2(-3)+1=-5$
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 $x=2$: $y=2(2)+1=5$

Step3: Calculate y for $4x-8=y$

For $x=1$: $y=4(1)-8=-4$
For $x=2$: $y=4(2)-8=0$
For $x=3$: $y=4(3)-8=4$

Step4: Calculate y for $y=x+1$

For $x=-4$: $y=-4+1=-3$
For $x=-3$: $y=-3+1=-2$
For $x=-2$: $y=-2+1=-1$
For $x=-1$: $y=-1+1=0$
For $x=0$: $y=0+1=1$
For $x=1$: $y=1+1=2$
For $x=2$: $y=2+1=3$
For $x=3$: $y=3+1=4$
For $x=4$: $y=4+1=5$

Step5: Summarize coordinate pairs

For $y=x-4$:

$(-1, -5), (0, -4), (1, -3), (2, -2), (3, -1)$

For $y=2x+1$:

$(-3, -5), (-2, -3), (-1, -1), (0, 1), (1, 3), (2, 5)$

For $4x-8=y$:

$(1, -4), (2, 0), (3, 4)$

For $y=x+1$:

$(-4, -3), (-3, -2), (-2, -1), (-1, 0), (0, 1), (1, 2), (2, 3), (3, 4), (4, 5)$

Step6: Graphing Instructions

Plot each coordinate pair on their respective grids, then draw a straight line through the points for each equation.

Answer:

Table for $y=x-4$:

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

Table for $y=2x+1$:

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

Table for $4x-8=y$:

$x$	$y$
2	0
3	4

Table for $y=x+1$:

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

To graph: Plot each set of (x,y) points on their grids and connect with a straight line.