Question

City planners want to construct a bike path perpendicular to Lome Lane at point P. An equation for the Lome Lane line is

Answer 1

Answer:

Equation of Lome lane → y = $-\frac{4}{5}x$

Equation of bike lane → y = $\frac{5}{4}x$

Step-by-step explanation:

Since, Lome lane line is passing through (0, 0) and (10, -8),

Slope of the line '$m_1$' = $\frac{y_2-y_1}{x_2-x_1}$

                                 = $\frac{0+8}{0-10}$

                                 = $-\frac{4}{5}$

y-intercept of the line = 0

Equation of the line will be,

y = $m_1x$

$y=-\frac{4}{5}x$

Since, bike path is perpendicular to the Lome lane line a point P,

By the property of perpendicular lines,

$m_1\times m_2=-1$

Where $m_2$ is the slope of the bike path.

$-\frac{4}{5}\times m_2=-1$

$m_2=\frac{5}{4}$

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 $\frac{5}{4}$ will be,

y - 0 = $\frac{5}{4}(x-0)$

y = $\frac{5}{4}x$

Equation of Lome lane → y = $-\frac{4}{5}x$

Equation of bike lane → y = $\frac{5}{4}x$