Which compound inequality is equivalent to the absolute value inequality ? –6 > b and b > 6 b > –6 or b < 6 –6 < b and b > 6 b < –6 or b > 6

The option 2  

b > -6 or b < 6 ⇒ |b| < 6    

Step-by-step explanation:

Given the compound inequality

we have to choose the inequality which is equivalent to the absolute value inequality.

An absolute value inequality

It is an inequality that has an absolute value sign with a variable inside.

In other words, for any real numbers x and y,

if | x | < y , then a < b and a > -b

Option 1: -6 > b and b > 6

Not possible as b can not be greater than 6 if it is less than -6

⇒ No solution exits

Option 2: b > -6 or b < 6

⇒ |b| < 6

which is absolute inequality.

Option 3: -6 < b and b > 6

This gives b is greater than 6 not an absolute inequality.

Option 4: b < –6 or b > 6

Not possible as b can not be greater than 6 if it is less than -6

⇒ No solution exits

Hence, option 2 is correct.

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is