Question

FOUR QUESTIONS!!! 15 POINTS!!! PLEASE HELP AND SHOW WORK

1) 0.2 (m - 8) = 0.3m + 5 - 3 + 0.3m


2) 3/2x - 2.2 = 2 (0.7x - 1)


3) 0.2 (2x + 1/2) = 5 [ 0.5 + (-2) ]


4) A line contains the points (5,3) and (0, -1). What is the equation of the line?

Answer 1

1. m=-4.5

2. See steps below

3. See steps below

4.
`y=(4)/(5)x-1`

Explanation:

1. To simplify equations, distribute terms into the parenthesis by multiplying each term. Then combine like terms and solve using inverse operations.

0.2(m-8) = 0.3m+5-3+0.3m

0.2m - 1.6 = 0.3m + 5 -3 + 0.3m

0.2m - 1.6 = 0.6m + 2

0.2m = 0.6m + 1.8

-0,4m = 1.8

m= -4.5

Apply these same steps to questions 2 and 3.

4. To write the equation of a line, find the slope using the slope formula. Then substitute the slope and a point into the point slope form.

`m=(y_2-y_1)/(x_2-x_1) =(3--1)/(5-0)=(3+1)/(5) =(4)/(5)`

`y-y_1 = m(x-x_1)\\y--1=(4)/(5)(x-0)\\y+1=(4)/(5)x\\y=(4)/(5)x-1`