Question

1. fill out the table with the correct values then graph the points.

a. y = -2x + 3
b. 2x + 3

in (x)

-4

-3

-2

-1

0

1

2

3

4

|out (y)|

in (x)

-4

-3

-2

-1

0

1

2

3

4

|out (y)|

Explanation:

Step1: Calculate values for \(y = - 2x+3\)

When \(x=-4\), \(y=-2\times(-4)+3=8 + 3=11\); when \(x = - 3\), \(y=-2\times(-3)+3=6 + 3=9\); when \(x=-2\), \(y=-2\times(-2)+3=4 + 3=7\); when \(x=-1\), \(y=-2\times(-1)+3=2 + 3=5\); when \(x = 0\), \(y=-2\times0+3=3\); when \(x = 1\), \(y=-2\times1+3=-2 + 3=1\); when \(x = 2\), \(y=-2\times2+3=-4 + 3=-1\); when \(x = 3\), \(y=-2\times3+3=-6 + 3=-3\); when \(x = 4\), \(y=-2\times4+3=-8 + 3=-5\).

Step2: Calculate values for \(y = 2x+3\)

When \(x=-4\), \(y=2\times(-4)+3=-8 + 3=-5\); when \(x=-3\), \(y=2\times(-3)+3=-6 + 3=-3\); when \(x=-2\), \(y=2\times(-2)+3=-4 + 3=-1\); when \(x=-1\), \(y=2\times(-1)+3=-2 + 3=1\); when \(x = 0\), \(y=2\times0+3=3\); when \(x = 1\), \(y=2\times1+3=2 + 3=5\); when \(x = 2\), \(y=2\times2+3=4 + 3=7\); when \(x = 3\), \(y=2\times3+3=6 + 3=9\); when \(x = 4\), \(y=2\times4+3=8 + 3=11\).

Answer:

For \(y=-2x + 3\), the \(y\)-values are \(11,9,7,5,3,1,-1,-3,-5\) corresponding to \(x=-4,-3,-2,-1,0,1,2,3,4\) respectively.
For \(y = 2x+3\), the \(y\)-values are \(-5,-3,-1,1,3,5,7,9,11\) corresponding to \(x=-4,-3,-2,-1,0,1,2,3,4\) respectively.
(Note: Graphing the points would involve plotting each \((x,y)\) - pair on the given coordinate - grids, but this text - based response can't actually create the graph. The points for \(y=-2x + 3\) are \((-4,11),(-3,9),(-2,7),(-1,5),(0,3),(1,1),(2,-1),(3,-3),(4,-5)\) and for \(y = 2x+3\) are \((-4,-5),(-3,-3),(-2,-1),(-1,1),(0,3),(1,5),(2,7),(3,9),(4,11)\))