If an equation of the linear function in the figure above is y = mx + b, than m = -2
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.
Since the figure is unknown, I will assume it is as shown in the attachment.
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]
From above equation , it can be concluded that if y = -2x + 2 , then m = -2 and b = 2
Grade: High School
Subject: Mathematics
Chapter: Linear Equations
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point
