<h2>Point ( 3,2 ) is one of the solution.</h2>
<h3>Further explanation</h3>
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 :
<em>m → gradient of the line</em>
<em>( 0 , c ) → y - intercept</em>
Gradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :
![\boxed {\large {m = \frac{y_2 - y_1}{x_2 - x_1}} }](https://tex.z-dn.net/?f=%5Cboxed%20%7B%5Clarge%20%7Bm%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D%7D%20%7D)
If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :
![\boxed {y - y_1 = m ( x - x_1 )}](https://tex.z-dn.net/?f=%5Cboxed%20%7By%20-%20y_1%20%3D%20m%20%28%20x%20-%20x_1%20%29%7D)
Let us tackle the problem.
This probem is about Linear Inequality.
<u>Given:</u>
<h2>y ≤ 2x − 4</h2>
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
<h3>Learn more</h3>
<h3>Answer details</h3>
Grade: High School
Subject: Mathematics
Chapter: Linear Equations
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point