Question

a. fill in the table to match the graph below.

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

b. which of the following points would be on the line? circle all that apply.
(-2,7) (6,-9) (-3,8) (10,-17)
c. write the equation of the line in slope - intercept form (y = mx + b)
6
find each difference.

1. -26 - (-30) 2. 25 - 32 3. -18 - 54 4. 59 - (-19)
2. -11 - (-10) 6. -20 - 13 7. 21 - (-56) 8. 15 - (-40)

Explanation:

Part a, b, c (Linear Line Questions)

Step1: Verify table values

From the table, check slope:
$m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-5}{0-(-2)}=\frac{-2}{2}=-2$
Check $y=mx+b$: use $(0,3)$, so $b=3$. Equation: $y=-2x+3$.
Verify table:
$x=-2$: $y=-2(-2)+3=5$ ✔️
$x=0$: $y=-2(0)+3=3$ ✔️
$x=1$: $y=-2(1)+3=1$ ✔️
$x=2$: $y=-2(2)+3=-1$ ✔️
$x=3$: $y=-2(3)+3=-3$ ✔️

Step2: Check valid points

Test each point in $y=-2x+3$:

1. $(-2,7)$: $y=-2(-2)+3=7$ ✔️
2. $(0,-2)$: $y=-2(0)+3=3

eq-2$ ❌

1. $(-3,8)$: $y=-2(-3)+3=9

eq8$ ❌

1. $(10,-17)$: $y=-2(10)+3=-17$ ✔️

Step3: Write slope-intercept form

Slope $m=-2$, y-intercept $b=3$, so:
$y=-2x+3$

Step1: Simplify each subtraction

Use rule: $a-(-b)=a+b$, $a-b=a+(-b)$

1. $-26-(-30)=-26+30=4$
2. $25-32=25+(-32)=-7$
3. $-18-54=-18+(-54)=-72$
4. $59-(-19)=59+19=78$
5. $-41-(-19)=-41+19=-22$
6. $-20-13=-20+(-13)=-33$
7. $31-(-56)=31+56=87$
8. $15-(-40)=15+40=55$

Answer:

a. The table values are already correct:

$x$	-2	0	1	2	3

b. Valid points:
A. $(-2,7)$, D. $(10,-17)$
c. $y=-2x+3$

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Part [6] (Subtraction Problems)