The solutions to the inequality y ≤ 2x − 4 are shaded on the graph. which point is a solution? (−1, 1) (1, −1) (3, 2) (2, 3)

(3,2)

Step-by-step explanation:

You can substitute or you can see which ordered pair is in the shaded area.

(-1,1):

y  ≤ 2x - 4

1 ≤ 2(-1) - 4

1 ≤ -2 - 4

1 ≤ -6

(-1,1) is NOT a solution.

(1,-1):

y ≤ 2x - 4

-1 ≤ 2(1) - 4

-1 ≤ 2 - 4

-1 ≤ -2

(1,-1) is NOT a solution.

(3,2):

y ≤ 2x - 4

2 ≤ 2(3) - 4

2 ≤ 6 - 4

2 ≤ 2

(3,2) IS a solution.

(2,3):

y ≤ 2x - 4

3 ≤ 2(2) - 4

3 ≤ 4 - 4

3 ≤ 0

(2,3) is NOT a solution.

Solving linear equation mean calculating the unknown variable from the equation.

Let the linear equation : y = mx + c

If we draw the above equation on Cartesian Coordinates , it will be a straight line with :

m → gradient of the line

( 0 , c ) → y - intercept

Gradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :

If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :

Let us tackle the problem.

This probem is about Linear Inequality.

Given:

To determine which point is a solution , we could plot the points on the graph. The point that is in the shaded region will be the solution.

Let: point A (-1,1) , B (1,-1) , C (3,2) , D (2,3).

As shown in the graph in the attachment, from the four known points, only point C(3,2) is inside the shaded area.

∴ Point C is one of the solution of y ≤ 2x − 4

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point