Question

Which inequality is represented by the graph? Which test point holds true for the inequality?

Answer 1

Answer:

see the explanation

Step-by-step explanation:

From the graph take two points

we have

(-1,4) and (1,1)

Find the slope

The formula to calculate the slope between two points is equal to

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

substitute

$m=\frac{1-4}{1+1}$

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

Find the equation of the solid line in slope point form

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

we have

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

$point\ (1,1)$

substitute

$y-1=-\frac{3}{2}(x-1)$

isolate the variable y

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

$y=-\frac{3}{2}x+\frac{5}{2}$

$y=-1.5x+2.5$

The solution of the inequality is the shaded area below the solid line

so

The equation of the inequality is

$y\leq -1.5x+2.5$

The solution is the shaded area below the solid line $y=-1.5x+2.5$

All points belonging to the shaded area including the boundary line are part of the solution of the inequality

Example

point (0,2.5)

substitute in the inequality

$2.5\leq -1.5(0)+2.5$

$2.5\leq 2.5$ ----> is true

therefore

The point hold true for the inequality