Question

Which point is a solution to the inequality shown in this graph

Answer 1

A solution would be (0,5)

it cannot be (3,3) or (-3,-1) because u have a dashed line...and it cannot be (0,0) because that is not in the solution area either

Answer 2

Step 1

Find the equation of the line of the inequality

Let

$A(-3,-1)\ B(3,3)$

Find the slope of the line

The slope is equal to

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

substitute the values

$m=\frac{3+1}{3+3}$

$m=\frac{4}{6}$

$m=\frac{2}{3}$

Find the equation of the line into point-slope form

$y-y1=m(x-x1)$

we have

$m=\frac{2}{3}$

$(x1,y1)=B(3,3)$

substitute in the equation

$y-3=\frac{2}{3}(x-3)$

$y=\frac{2}{3}x-2+3$

$y=\frac{2}{3}x+1$

Find the equation of the inequality

The solution is the shaded area above the dotted line

so the inequality is

$y>\frac{2}{3}x+1$

If a point is the solution of the inequality, then it must satisfy the inequality. Let's check each of the points

Step 2

case A) $(0,0)$

Substitute the values of x and y in the inequality

$x=0\ y=0$

$0>\frac{2}{3}*0+1$

$0>1$-----> is not true

therefore

the point $(0,0)$ is not solution of the inequality

Step 3

case B) $(3,3)$

Substitute the values of x and y in the inequality

$x=3\ y=3$

$3>\frac{2}{3}*3+1$

$3>3$-----> is not true

therefore

the point $(3,3)$ is not solution of the inequality

Step 4

case C) $(-3,-1)$

Substitute the values of x and y in the inequality

$x=-3\ y=-1$

$-1>\frac{2}{3}*-3+1$

$-1>-1$-----> is not true

therefore

the point $(-3,-1)$ is not solution of the inequality

Step 5

case D) $(0,5)$

Substitute the values of x and y in the inequality

$x=0\ y=5$

$5>\frac{2}{3}*0+1$

$5>1$-----> is true

therefore

the point $(0,5)$ is a solution of the inequality

therefore

the answer is

$(0,5)$