Question

Write the equation of the line which passes through (2, –3) and is perpendicular to y = 4x + 7 in standard form.

Answer 1

begin by finding the slope of y=4x+7

Answer 2

a clue please

Answer 3

look up the slope intercept equation of the line and the point-slope equation of the line.

Answer 4

slope intercept is y=mx+b

Answer 5

and point slope equation is y - y1 = m(x - x1)

Answer 6

So to find the equation of the new line we need a point (which we have) and a slope

Answer 7

To find the slope of the new line we have to find the slope of the line given in the problem statement. This is because we know that the new line is perpendicular to the old line.

Answer 8

Therefore, we need to find the slope of the old line from the equation y=4x+7 (which happens to be in slope-intercept form). What is the slope of the line given by y=4x+7?

Answer 9

y=4x+7 = y-7=4x ?

Answer 10

:(

Answer 11

for this step we just have to recognize that y=4x+7 is in the same form as y=mx+b

Answer 12

it is as y=mx+b

Answer 13

To identify the slope you need to match up what number is in the space where the 'm' is. m in these equations stands for slope.

Answer 14

oh yea!

Answer 15

y = 4(2)+7

Answer 16

y=8+7

Answer 17

y=15

Answer 18

no, we don't need to use the point yet.

Answer 19

:(

Answer 20

all we are doing first is identifying the slope of the line.

Answer 21

y=mx+b has a slope of m
so
y=4x+7 has a slope of ???

Answer 22

y !

Answer 23

nope, the slope would be 4 since, four is in the corresponding space as the m in the first equation

Answer 24

omg :( you are right

Answer 25

y=mx+b has a slope of m

y=4x+b has a slope of 4

Since the four and the m are in the same spots!

Answer 26

:D

Answer 27

now, do you know the equation to find a perpendicular slope?

Answer 28

mmm im not sure is it y2-y1/x2-x1 ?

Answer 29

that is the equation of the slope, given two points.

Answer 30

right now we are going to calculate the perpendicular slope given any slope.

Answer 31

Right now we have figured out the slope of the given line, which was 4. The perpendicular slope to 4 is the negative reciprocal of 4.

Answer 32

\[perpendicular slope=\frac{-1}{m}=\frac{-1}{4}\]

Answer 33

-1/4=-1/4

Answer 34

so what do we do now ?

Answer 35

we now have the slope of the line that we are interested in!

Answer 36

this means that we have the point and the slope of the new line that we are interested in. This means we can use the point-slope equation of the line.

Answer 37

yay ! okay so y - y1 = m(x - x1)?

Answer 38

yes, the m is the slope, y1 is the y point and x1 is the x point from (2, -3)

Answer 39

2+3 = 4( :s ) ? :0

Answer 40

what you do for this equation is to plug in m=-1/4; y1=-3; x1=2
leave the rest of the equation the same.

Answer 41

1+3=-1/4(1-2)

Answer 42

y + 3 = (-1/4)*(x - 2)
do you see how i kept everything the same except for replacing y1, x1, and m?

Answer 43

yea :0 i though i had to replace it all

Answer 44

no, when we are looking for the equation of the line, we have to keep x and y.

Answer 45

Now you need to look up the Standard Form

Answer 46

:s Ax + By = C ?

Answer 47

yup, in the standard form A, B, and C have to be integers. Soooooo, the last step that we have to do is change
y + 3 = (-1/4)*(x-2)
into the form of
Ax+By=C

Answer 48

This is just algebra, begin by multiplying y+3 = (-1/4)*(x-2) by four on both sides.

Answer 49

y+3= -1/4x - 2.25 ?

Answer 50

@juantweaver ?