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3 years ago

Write the equation of the line perpendicular to y = 5/3x + 1 that passes through the point (- 8, 2)

Mathematics

1 answer:

xenn [34]3 years ago

4 0

Answer:

y = - $\frac{3}{5}$ x - $\frac{14}{5}$

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = $\frac{5}{3}$ x + 1 ← is in slope- intercept form

with slope m = $\frac{5}{3}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{5}{3} }$ = - $\frac{3}{5}$ , thus

y = - $\frac{3}{5}$ x + c ← is the partial equation

To find c substitute (- 8, 2) into the partial equation

2 = $\frac{24}{5}$ + c ⇒ c = 2 - $\frac{24}{5}$ = - $\frac{14}{5}$

y = - $\frac{3}{5}$ x - $\frac{14}{5}$ ← equation of perpendicular line

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