On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 2) and (2, 0). Everything to the left of the line is shaded. The second dashed line has a negative slope and goes through (0, 2) and (4, 0). Everything below and to the left of the line is shaded.
Which system of linear inequalities is represented by the graph?

y > x – 2 and x – 2y < 4
y > x + 2 and x + 2y < 4
y > x – 2 and x + 2y < 4
y > x – 2 and x + 2y < –4

sohiby

Step-by-step explanation:

The general equation of a straight line is given by:

Being given two points, we can replace x and y, solve the system and find the values for a and b.

The first line:

The problem states that it goes through

So, when . Replacing in the equation

For now, the equation of the line is:

The line also goes through . So, when . Replacing in the equation:

So, the equation of this line is:

Everything above the line is shaded.  So, it is represented by the following inequality:

The second line:

The problem states that it goes through

So, when . Replacing in the equation

The line also goes through . So, when . Replacing in the equation:

So, the equation of the line is:

Everything to the right of the line is shaded:

We have to write this in function of x:

Step-by-step explanation:

HOPE THIS HELPS

if a = 1,   and b = 2, then the answer is 47.99999999. if you round that to the nearest whole number, the answer is 48.

x = 12

y = 1

for the points!