Question

What system of inequalities is represented by the graph?

Answer 1

Answer:

$y\geq -5x+2$

$y\leq 3x-4$

Step-by-step explanation:

To write a linear inequalities we use the same guidelines as linear equations. They are written in the form, $y$ and  $y>mx +b$ or with any other inequality signs.

One line has y-intercept 2 and slope is -5/1 (down 5 and over 1).

This means the equation is

$y\leq -5x+2\\or\\y\geq -5x+2$.

Test a point not on the line to determine the direction of the inequality sign.

(0,0)

$y\leq -5x+2\\0\leq -5(0)+2\\0\leq 2$ This is true but not the equation becasue (0,0) is not shaded.

The other line has y-intercept -4 and slope 3/1 (up 3 and over 1).

This means the equation is

$y\leq 3x-4\\or\\y\geq 3x-4$.

Test a point not on the line to determine the direction of the inequality sign.

(0,0)

$y\leq 3x-4\\0\leq 3(0)-4\\0\leq -4$ This is false and the equation since (0,0) is not in the shaded portion.

Answer 2

Answer:

Equations are y ≥ -5x + 2 and y ≥ 3x -4.

Step-by-step explanation:

Given : Graph .

To find : What system of inequalities is represented by the graph.

Solution : We have given that graph with two lines.

We can see line 1 and line 2 both are shaded up and solid line that mean equations have equal or greater than sign .

We can see y - intercept ( line cut at y axis) of line 1 is 2 ans slope is -5.

Line of equation y = mx  + b

Where, m = slope and b = y -intercept.

Plug the values

y ≥ -5x + 2   ( greater than or equal to sign for solid line and shaded up).

In line 2 slope is 3 and y - intercept is -4.

Then equation become y ≥ 3x -4.  ( greater than or equal to sign for solid line and shaded up).

Therefore, Equations are y ≥ -5x + 2 and y ≥ 3x -4.