Respuesta :
Answer:
[tex] y= -\frac{6}{5} x +\frac{262}{5}[/tex]
[tex] y= -\frac{6}{5} x 89[/tex]
Step-by-step explanation:
For this case we need to remember that a line is defined with minimum two points. And for this case we have two points given and we want to find a line who fits for the two points.
The two points are (2,50) and (20,65). Let's define some notation:
[tex] x_1 = 2, y_1 = 50 , x_2 = 20, y_2 = 65[/tex]
We want to estimate a line [tex] y = mx+b[/tex]
Where m is the slope and b the the intercept. We can find the slope with the following formula:
[tex] m = \frac{\Delta y}{\Delta x} = \frac{y_2 -y_1}{x_2 -x_1}= \frac{65-50}{20-2}=\frac{5}{6}[/tex]
On this case we need "The lanes are perpendicular to a segment of the track", so for this case when we have perpendicular lines we need to satisfy this:
[tex] m_1 *m_2 = -1[/tex]
And if we find the slope for the tangent line [tex]m_2[/tex] we got:
[tex] \frac{5}{6} *m_2 = -1[/tex]
[tex] m_2 = -\frac{6}{5}[/tex]
Now with the slope we can find the value of b using the first point, on this case (2,50) and if we replace into our equation we got:
[tex] 50 = -\frac{6}{5} (2) + b[/tex]
And we can solve for b like this:
[tex] b = 50 + \frac{12}{5}=\frac{262}{5}[/tex]
And the first line perpendicular to the point (2,50) would be:
[tex] y= -\frac{6}{5} x +\frac{262}{5}[/tex]
Now with the slope we can find the value of b using the second point, on this case (20,65) and if we replace into our equation we got:
[tex] 65 = -\frac{6}{5} (20) + b[/tex]
And we can solve for b like this:
[tex] b = 65 + 24=89[/tex]
And the first line perpendicular to the point (20,65) would be:
[tex] y= -\frac{6}{5} x 89[/tex]
