Question

Which of the following inequalities matches the graph? 100 point

Answer 1

`\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }`

`\huge\underline{\sf{\red{Problem:}}}`

• Which of the following inequalities matches the graph?

`\underline{\sf{\red{Fomula \:for\:linear\:equation:}}}`

`\quad\quad\quad\quad\sf{y = \: mx + b }`

• We have two points which is (2,3)(0,7) and we need to find the slope first.

`\underline{\sf{\red{Fomula \: for \: slope:}}}`

`\quad\quad\quad\quad\sf{m = \frac{ \small{y} \tiny{2 } - \small{y} \tiny{1}}{\small{x} \tiny{2 } - \small{x} \tiny{1}} }`

• Let's Substitute it.

`\quad\quad\quad\quad\sf{m = (3 - 7)/(2 - 0) }`

`\quad\quad\quad\quad\sf{m = ( - 4)/(2) }`

`\quad\quad\quad\quad\sf{ \boxed{ \sf{m = - 2} }}`

`\underline{\sf{\red{Solution \: for \: y \: intercept:}}}`

`\quad\quad\quad\quad\sf{y = \: mx + b }`

`\quad\quad\quad\quad\sf{y = \: (- 2) + ( - 5) }`

`\quad\quad\quad\quad \boxed{\sf{y = 7 }}`

`\underline{\sf{\red{Answer \: for \: inequality:}}}`

`\huge\quad\quad \underline{\boxed{\sf{ \red{y < - 2x + 7 }}}}`

`\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }`

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✍︎ C.Rose❀

Answer 2

`\huge \boxed{ \boxed{\tt y < - 2x + 7 }}`

Explanation:

to understand this

you need to know about:

• linear inequality

tips and formulas:

• linear equation:y=mx+b
• 
  `m = ( y_(2) - y_(1))/( x_(2) - x_(1))`

let's solve:

let's figure out the slope

two points (2,3),(0,7)

`m = ( 3 - 7 )/( 2 - 0)`

`m = ( - 4)/(2)`

`m = - 2`

y-intercept:7

therefore

our linear inequality is

`\tt y < - 2x + 7`