Question

4 solve the following equations
-8 + 8x = 20
6(74 - 10) = 24
18 = 8b - 6 + b
10x - 16 = 44
5 use the graph on the right to answer the following questions:
a. fill in the table to match the graph below.

x	-1	0	1	2	3
y

b. which of the following points would be on the line? circle all that apply.
(-5, 7) (0, -3) (3, 0) (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)
5. -41 - (-19)
6. -20 - 13
7. 31 - (-50)
8. 15 - (-40)

Explanation:

Section [4]: Solve the equations

Step1: Solve $-8x + 9x = 20$

Combine like terms:
$(-8+9)x = 20$
$x = 20$

Step2: Solve $3b = 6b - 6 + b$

Combine like terms on right:
$3b = 7b - 6$
Subtract $7b$ from both sides:
$3b -7b = -6$
$-4b = -6$
Divide by $-4$:
$b = \frac{-6}{-4} = \frac{3}{2}$

Step3: Solve $6(7k - 10) = 24$

Divide both sides by 6:
$7k - 10 = \frac{24}{6} = 4$
Add 10 to both sides:
$7k = 4 + 10 = 14$
Divide by 7:
$k = \frac{14}{7} = 2$

Step4: Solve $10x - 16 = 44$

Add 16 to both sides:
$10x = 44 + 16 = 60$
Divide by 10:
$x = \frac{60}{10} = 6$

First, identify the line's equation from the graph: it passes through $(0,3)$ (y-intercept, $b=3$) and $(1,1)$, so slope $m=\frac{1-3}{1-0}=-2$. Equation: $y=-2x+3$

Part a: Fill the table

Substitute each $x$ into $y=-2x+3$:

• $x=-1$: $y=-2(-1)+3=2+3=5$
• $x=0$: $y=-2(0)+3=3$
• $x=1$: $y=-2(1)+3=1$
• $x=2$: $y=-2(2)+3=-4+3=-1$
• $x=3$: $y=-2(3)+3=-6+3=-3$

Part b: Check valid points

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

• $(-2,7)$: $7=-2(-2)+3=4+3=7$ ✔️
• $(0,-3)$: $-3

eq-2(0)+3=3$ ❌

• $(-3,9)$: $9=-2(-3)+3=6+3=9$ ✔️
• $(10,-17)$: $-17=-2(10)+3=-20+3=-17$ ✔️

Part c: Slope-intercept form

From above, slope $m=-2$, y-intercept $b=3$, so equation is $y=-2x+3$

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

Step1: Calculate $-26 - (-30)$

$-26 + 30 = 4$

Step2: Calculate $25 - 32$

$25 - 32 = -7$

Step3: Calculate $-18 - 54$

$-18 - 54 = -72$

Step4: Calculate $59 - (-19)$

$59 + 19 = 78$

Step5: Calculate $-41 - (-19)$

$-41 + 19 = -22$

Step6: Calculate $-20 - 13$

$-20 - 13 = -33$

Step7: Calculate $31 - (-56)$

$31 + 56 = 87$

Step8: Calculate $15 - (-40)$

$15 + 40 = 55$

Answer:

1. $x=20$
2. $b=\frac{3}{2}$
3. $k=2$
4. $x=6$

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Section [5]: Linear Graph Questions