The correct inequality for the graph below is y ≤ -2x + 2
Further explanation
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 :
[tex]\large {m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :
[tex]y - y_1 = m ( x - x_1 )[/tex]
Let us tackle the problem.
First, let us find the equation of solid line passing through points (0 , 2) and (1, 0) by using this formula :
[tex]\frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1}[/tex]
[tex]\frac{y - 2}{0 - 2} = \frac{x - 0}{1 - 0}[/tex]
[tex]\frac{y - 2}{- 2} = \frac{x}{1}[/tex]
[tex]1 (y - 2) = -2 (x)[/tex]
[tex]y - 2 = -2x[/tex]
[tex]\large {\boxed {y = -2x + 2} }[/tex]
If the shading is down part , then we can use a point test to determine the appropriate inequality.
Let the point test is ( 0,0 ) , then :
y ... -2x + 2
0 ... -2(0) + 2
0 ... 0 + 2
0 ... 2
0 < 2
Because 0 < 2 , then the correct inequality for down part shading is :
y ≤ -2x + 2
Learn more
- Infinite Number of Solutions : https://brainly.com/question/5450548
- System of Equations : https://brainly.com/question/1995493
- System of Linear equations : https://brainly.com/question/3291576
Answer details
Grade: High School
Subject: Mathematics
Chapter: Linear Equations
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point
