Which linear inequality is represented by the graph? y > 2x + 2 y ≥ x + 1 y > 2x + 1 y ≥ x + 2

Asked by maham237 @ 22/12/2020 in Mathematics viewed by 337 People

Which linear inequality is represented by the graph?
y > 2x + 2
y ≥ x + 1
y > 2x + 1
y ≥ x + 2

Answered by maham237 @ 22/12/2020

Step 1

Find the slope of the line

Let

$A(0,1)\\B(2,5)$

the slope is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{5-1}{2-0}$

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

$m=2$

Find the equation of the line

we know that

the equation of the line into slope-intercept form is

$y=mx+b$

where

m is the slope

b is the y-intercept

in this problem we have

$m=2$

$b=1$ ------> the y-intercept is the point A

substitute

$y=2x+1$

Step 2

Find the equation of the inequality

we know that

the solution is the shaded area above the dotted line

above dotted line---------> represent the symbol ( $>$ )

the inequality is

$y>2x+1$

therefore

the answer is

$y>2x+1$

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