Answer:
y = [tex]-\frac{2}{9}x+\frac{61}{9}[/tex]
Step-by-step explanation:
Let the equation of the new railroad track passing through the point [tex](x_1,y_1)[/tex] and slope = m₁ is,
[tex]y-y_1=m_1(x-x_1)[/tex]
Slope of the given line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope of the line passing through (-3, 1) and (6, -1) will be,
m₂ = [tex]\frac{1+1}{-3-6}[/tex]
m₂ = [tex]-\frac{2}{9}[/tex]
Since, railroad track and the given line are parallel,
m₁ = m₂ = [tex]-\frac{2}{9}[/tex]
Therefore, equation of the railroad track passing through (8, 5) and slope = [tex]-\frac{2}{9}[/tex] will be,
y - 5 = [tex]-\frac{2}{9}(x-8)[/tex]
y = [tex]-\frac{2}{9}x+\frac{16}{9}+5[/tex]
y = [tex]-\frac{2}{9}x+\frac{61}{9}[/tex]
