Question

13. Find the slope Intercept equation of the line passing through the point 2, 1) with a slope of m - 3. 14. Amanda has $12,000 in her savings account. If she deposits $325 every month into savings, how many months will It take her to save $22,000? Round your an swer to the nearesttenth. 15. Solve the Inequality. Give the result in set notation. 2(x + 3) + 4x - 4 <8x 16. Find the product. Give your answer in a + bilarm. (2 - 302

Answer 1

SOLUTION

13

The standard form of linear equation

y = mx + b

where,

m=slope

b=intercept

Put the value of slope m = 3 in equation y =mx + b

y = 3x + b

Now,

Put (2, 1), x=2, y = 1

i.e,

1=3.2 + b

1= 6 + b

b=1-6

9- = 4

So,

b = intercept = -5

Therefore,

m = slope = 3

b = intercept = -5

The line equation y = mx + b, where m = 3 and b = -5

y = 3x - 5

14

According to question,

Total Savings amount = Present amount in savings account + (Amount deposited per month ) * (Number of months)

$22000 = $12000+ $325 x Number of months)

$22000 – $12000 = $325 x Number of months)

$10000 = $325 (Number of months)

Number of months = $10000 $325

Number of months = 10000 325

Number of months = 30.76923077

Number of months 31

Therefore,

It will take her 31 months.

15

2(x + 3) + 4x – 4 < 8x

2x + 6 + 4x – 4 < 8x

→ 6x + 2 < 8x

Subtract 2 from both sides

→ 6x + 2 – 2 < 8x – 2

нбх <8x – 2

Subtract 8x from both sides

+ 6x – 8x < 8x – 2 – 8x

→ -2x < -2

Multiply both sides by – 1 (reverse the inequality)

${-2x) (-1)>(-2)(-1)

2x > 2

Divide both sides by 2

V

X>1

Therefore,

Solution : x>1 Interval Notation : (1, 0)

16

(2-3)

(a - b)? = a? – 2ab + b

a = 2, b=31

= 2 -2.2.3i + (31)

-4-12749中

= -1

-4-12j + (-1)

-4-12 -9

= -5-12

Therefore,

(2-31) = -5-127