Question

Find the equation of the line through point (1,−5) and perpendicular to y=1/8x+2. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for 12).

Answer 1

Answer:

$y = -8x + 3$

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

$y = mx + b$

In which m is the slope and b is the y-intercept.

Perpendicular lines:

When two lines are perpendicular, the multiplication of their slopes is -1.

Perpendicular to y=1/8x+2

This line has slope $\frac{1}{8}$

So, for the line we want to find the equation, we have that:

$\frac{m}{8} = -1$

$m = -8$

So

$y = -8x + b$

Find the equation of the line through point (1,−5)

This means that when $x = 1, y = -5$. We use this to find b. So:

$y = -8x + b$

$-5 = -8 + b$

$b = 3$

The equation of the line is:

$y = -8x + 3$