Question

Find the equation of the line through point (−5,5) and perpendicular to y=5/9x−4. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for 1/2).

Answer 1

Answer:

$y = -9/5x-4$

Step-by-step explanation:

Given

Passes through $(-5,5)$

Perpendicular to $y = 5/9x - 4$

Required

The line equation

First, we calculate its slope (m)

In $y = 5/9x - 4$, the slope is:

$m =5/9$

This is so because, the gradient intercept is:

$y = mx + b$

By comparison, you have: $m =5/9$

Since the required line and $y = 5/9x - 4$ are perpendicular, then the slope (m2) is:

$m_2 = -1/m$

$m_2 = -1/(5/9)$

$m_2 = -9/5$

The equation is then calculated using:

$y = m(x - x_1) + y_1$

$y = -9/5(x - (-5)) + 5$

$y = -9/5(x +5) + 5$

$y = -9/5x-9 + 5$

$y = -9/5x-4$