2 Answers

Vivek Parihar · Answer 1 · 2022-02-18T02:30:47+0000

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

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

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.

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

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

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

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

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

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

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

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

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

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