Answer :
Answer: The equation that represents the road is y= - 1/3x +1/3
Step-by-step explanation:
The perpendicular equation that represents the road that passes through the point is [tex]\mathbf{y = -\frac 13x + \frac 13 }[/tex]
The points of the red line (see attachment) are given as:
[tex]\mathbf{(x,y) = (0,2), (2,8)}[/tex]
Start by calculating the slope (m) of the line using:
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 -x_1}}[/tex]
So, we have:
[tex]\mathbf{m = \frac{8 - 2}{2 -0}}[/tex]
[tex]\mathbf{m = \frac{6}{2}}[/tex]
[tex]\mathbf{m = 3}[/tex]
Next, calculate the slope (m2) of the perpendicular line using:
[tex]\mathbf{m_2 = -\frac 1m}[/tex]
So, we have:
[tex]\mathbf{m_2 = -\frac 13}[/tex]
The perpendicular line passes through point (1,0).
So, the line equation is calculated using:
[tex]\mathbf{y = m_2(x - x_1) + y_1}[/tex]
This gives
[tex]\mathbf{y = -\frac 13(x - 1) + 0}[/tex]
[tex]\mathbf{y = -\frac 13(x - 1) }[/tex]
Open bracket
[tex]\mathbf{y = -\frac 13x + \frac 13 }[/tex]
Hence, the line equation is [tex]\mathbf{y = -\frac 13x + \frac 13 }[/tex]
Read more about perpendicular equations at:
https://brainly.com/question/21740769
