Question

A line passes through the point (–2, 4), and its y-intercept is (0, –6). What is the equation of the line that is perpendicular to the first line and passes through the point (5, –4)?

Answer 1

HI!!

Answer 2

first find the slope
do you know how to do that?

Answer 3

y- y1 = m (x-x1)

Answer 4

no dear that is the point - slope formula
you need the slope first, then you can use that one

Answer 5

then i dont know how to find the slope

Answer 6

\[\frac{y_2-y_1}{x_2-x_1}\] with
\[x_1=-2,y_1=4,x_2=0,y_2=-6\]

Answer 7

so the slope is -5/1

Answer 8

or you can reason as follows
from -2 to 0 is right 2 units
from 4 to -6 is down ten
right 2, down 10 slope is \(-\frac{10}{5}=-5\)

Answer 9

now you need the slope of the perpendicular line
that will be the "negative reciprocal" of \(-5\) which is \(\frac{1}{5}\)

Answer 10

NOW you can use the point slope formula with the slope \(m=\frac{1}{5}\) and the point \((5,-4)\)

Answer 11

so y- -4 = 1/5 (x - 5)?

Answer 12

So the anser would be y = 1/5x - 5