Answer:
The equation of Grant's path is y = 4 - x over 2 ⇒ 2nd answer
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
- m is the slope of the line
- b is the y-intercept (value y at x = 0)
The formula of the slope of a line is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
∵ Grant's path is a line from point A to point B
∴ The equation of AB represents Grant's path
Lets find the slope of AB using the formula of the slope above
∵ A = (8 , 0)
∵ B = (-4 , 6)
∴ [tex]x_{1}[/tex] = 8 and [tex]x_{2}[/tex] = -4
∴ [tex]y_{1}[/tex] = 0 and [tex]y_{2}[/tex] = 6
∵ [tex]m=\frac{6-0}{-4-8}=\frac{6}{-12}[/tex]
∴ [tex]m=-\frac{1}{2}[/tex]
Substitute the value of m in the form of the equation
∵ y = m x + b
∴ y = [tex]-\frac{1}{2}[/tex] x + b
∵ b is the value of y at x = 0
∵ y = 4 at x = 0 ⇒ from the figure
∴ b = 4
∴ y = [tex]-\frac{1}{2}[/tex] x + 4
We can write [tex]-\frac{1}{2}[/tex] x as [tex]-\frac{x}{2}[/tex]
∴ y = [tex]-\frac{x}{2}[/tex] + 4
- Switch the two terms of the right hand side
∴ y = 4 - [tex]\frac{x}{2}[/tex]
The equation of Grant's path is y = 4 - [tex]\frac{x}{2}[/tex]
