The equation that represents the line shown in the graph is:
B. y = -3x + 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 {\boxed {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]\large {\boxed {y - y_1 = m ( x - x_1 )} }[/tex]
Let us tackle the problem!
From the graph , the line goes through the point ( -1 , 5 ) and ( 0 , 2 ).
Let:
( x₁ , y₁ ) = ( 0 , 2 )
( x₂ . y₂ ) = ( -1 , 5 )
[tex]\texttt{ }[/tex]
We can calculate the gradient of the graph by using this following formula:
[tex]m = ( y_2 - y_1 ) \div ( x_2 - x_1 )[/tex]
[tex]m = ( 5 - 2 ) \div ( -1 - 0 )[/tex]
[tex]m = 3 \div (-1)[/tex]
[tex]m = -3[/tex]
[tex]\texttt{ }[/tex]
Next , we can find the equation of the graph by using this following formula:
[tex]y - y_1 = m ( x - x_1 )[/tex]
[tex]y - 2 = -3 ( x - 0 )[/tex]
[tex]y - 2 = -3x[/tex]
[tex]y = -3x + 2[/tex]
[tex]\texttt{ }[/tex]
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
