Answer:
Equation of Lome lane → y = [tex]-\frac{4}{5}x[/tex]
Equation of bike lane → y = [tex]\frac{5}{4}x[/tex]
Step-by-step explanation:
Since, Lome lane line is passing through (0, 0) and (10, -8),
Slope of the line '[tex]m_1[/tex]' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{0+8}{0-10}[/tex]
= [tex]-\frac{4}{5}[/tex]
y-intercept of the line = 0
Equation of the line will be,
y = [tex]m_1x[/tex]
[tex]y=-\frac{4}{5}x[/tex]
Since, bike path is perpendicular to the Lome lane line a point P,
By the property of perpendicular lines,
[tex]m_1\times m_2=-1[/tex]
Where [tex]m_2[/tex] is the slope of the bike path.
[tex]-\frac{4}{5}\times m_2=-1[/tex]
[tex]m_2=\frac{5}{4}[/tex]
Equation of line passing through (x', y') and slope 'm' is given by,
y - y' = m(x - x')
Since, bike path passes through (0, 0) and slope [tex]\frac{5}{4}[/tex] will be,
y - 0 = [tex]\frac{5}{4}(x-0)[/tex]
y = [tex]\frac{5}{4}x[/tex]
Equation of Lome lane → y = [tex]-\frac{4}{5}x[/tex]
Equation of bike lane → y = [tex]\frac{5}{4}x[/tex]
