Question

Which of the following inequalities matches the graph? 100 point

Answer 1

Answer:

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

Step-by-step explanation:

to understand this

you need to know about:

• linear inequality

tips and formulas:

• linear equation:y=mx+b
• $m = \frac{ y_{2} - y_{1}}{ x_{2} - x_{1}}$

let's solve:

let's figure out the slope

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

$m = \frac{ 3 - 7 }{ 2 - 0}$

$m = \frac{ - 4}{2}$

$m = - 2$

y-intercept:7

therefore

our linear inequality is

$\tt y < - 2x + 7$

Answer 2

$\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

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

• 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.

$\quad\quad\quad\quad\sf{m = \frac{3 - 7}{2 - 0} }$

$\quad\quad\quad\quad\sf{m = \frac{ - 4}{2} }$

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

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

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

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

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

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

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

$\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

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✍︎ C.Rose❀