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Which of the following inequalities matches the graph? 100 point

Which Of The Following Inequalities Matches The Graph 100 Point class=

Sagot :

Nayefxidn

Answer:

[tex] \huge \boxed{ \boxed{\tt y < - 2x + 7 }}[/tex]

Step-by-step explanation:

to understand this

you need to know about:

  • linear inequality

tips and formulas:

  • linear equation:y=mx+b
  • [tex]m = \frac{ y_{2} - y_{1}}{ x_{2} - x_{1}}[/tex]

let's solve:

let's figure out the slope

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

[tex]m = \frac{ 3 - 7 }{ 2 - 0}[/tex]

[tex]m = \frac{ - 4}{2} [/tex]

[tex]m = - 2[/tex]

y-intercept:7

therefore

our linear inequality is

[tex] \tt y < - 2x + 7[/tex]

View image Nayefx

[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]

[tex]\huge\underline{\sf{\red{Problem:}}}[/tex]

  • Which of the following inequalities matches the graph?

[tex]\underline{\sf{\red{Fomula \:for\:linear\:equation:}}}[/tex]

[tex]\quad\quad\quad\quad\sf{y = \: mx + b }[/tex]

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

[tex]\underline{\sf{\red{Fomula \: for \: slope:}}}[/tex]

[tex]\quad\quad\quad\quad\sf{m = \frac{ \small{y} \tiny{2 } - \small{y} \tiny{1}}{\small{x} \tiny{2 } - \small{x} \tiny{1}} }[/tex]

  • Let's Substitute it.

[tex]\quad\quad\quad\quad\sf{m = \frac{3 - 7}{2 - 0} }[/tex]

[tex]\quad\quad\quad\quad\sf{m = \frac{ - 4}{2} }[/tex]

[tex]\quad\quad\quad\quad\sf{ \boxed{ \sf{m = - 2} }}[/tex]

[tex]\underline{\sf{\red{Solution \: for \: y \: intercept:}}}[/tex]

[tex]\quad\quad\quad\quad\sf{y = \: mx + b }[/tex]

[tex]\quad\quad\quad\quad\sf{y = \: (- 2) + ( - 5) }[/tex]

[tex]\quad\quad\quad\quad \boxed{\sf{y = 7 }}[/tex]

[tex]\underline{\sf{\red{Answer \: for \: inequality:}}}[/tex]

[tex] \huge\quad\quad \underline{\boxed{\sf{ \red{y < - 2x + 7 }}}}[/tex]

[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]

#CarryOnLearning

✍︎ C.Rose❀

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