Question

On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (2, negative 1). Everything to the left of the line is shaded. Which linear inequality is represented by the graph? y > 2x + 3 y < 2x + 3 y > −2x + 3 y < −2x + 3

Answer 1

Answer:

The answer to your question is    y < -2x + 3

Step-by-step explanation:

See the graph below

Process

1.- Find the slope

   $m = \frac{y2 - y1}{x2 - x1}$

Substitution

   $m = \frac{-1 - 3}{2 - 0}$

   $m = \frac{-4}{2}$

   $m = -2$

2.- Find the equation of the line

   y - y1 = m(x - x1)

Substitution

  y - 3 = -2(x - 0)

Simplify and solve for y

  y - 3 = -2x

  y = -2x + 3

3.- Write the inequality

As the left area of the plane is shaded the inequality must be

 y < -2x + 3

   

Answer 2

Answer:

$y$

Step-by-step explanation:

First, we use the given points to find the slope of such line.

The formula to find the slope is

$m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }$

In this case, the points are (0,3) and (2,-1).

$m=\frac{-1-3}{2-0}=-\frac{4}{2}=-2$

Then, we use the point-slope formula to find the equation

$y-y_{1} =m(x-x_{1} )\\y-3=-2(x-0)\\y=-2x+3$

Now, notice that everything to the left of the line is shaded, that means the origin must be part of the solutions.

Therefore, the right inequality is

$y$

(The image attached shows the graph)