Question

In the xy- plane, line q and r are parallel. Line q passes through the point (3, 7), and line r passes through the point (3, 2). If the y-intercept for line r is -2, what is the equation of a line perpendicular to line q, which intersects line q on the y-axis?
(a) y= 4/3x + 3
(b) y= -3/4x + 3
(c) y= -4/3x + 11
(d) y= 4/3x + 11
(e) -3/4x + 11

Answer 1

since q and r are parallel lines they have the same slope. so
\[ \large \text{q:}\qquad y-7=m(x-3) \]
\[ \large \text{r:}\qquad y-2=m(x-3) \]

Answer 2

ok?

Answer 3

ok

Answer 4

for line r u r told that the y-intercept is -2.
this means that when x=0 then y=-2

Answer 5

alright

Answer 6

in the equation for r replace x=0 and y=-2 and find the value of m.
try it!

Answer 7

wait what's the equation?

Answer 8

i posted it before

Answer 9

oh sorry yeah

Answer 10

it is my first post

Answer 11

-4 = m(0-3)

Answer 12

yes. find m

Answer 13

4/3 ?

Answer 14

great

Answer 15

this means that the equation for line q is
\[ \large \text{q:}\quad y-7=\frac{4}{3}(x-3) \]

Answer 16

ok?

Answer 17

yes

Answer 18

it can be rewrittren into
\[ \large y-7=\frac{4}{3}x-4 \]
or
\[ \large y=\frac{4}{3}x+3 \]
(slope-intercept form)

Answer 19

got it?

Answer 20

yeah thanks

Answer 21

now finally. u r asked for line perpendicular to this one that passes through the y-intercept of q (its intersection with the y-axis)

Answer 22

the y-intercept of q is (0,4)

Answer 23

q has slope m=4/3 the new line has slope m1 such that
\[ \large m_1\times m=-1 \]
what would be the value of m1?

Answer 24

is the new slope -3/4

Answer 25

yes so the line requested would be
\[ \large y-4=-\frac{3}{4}(x-0) \]

Answer 26

sorry. made a mistake

Answer 27

the y-intercept is (0,3)

Answer 28

then the equation is
\[ \large y-3=-\frac{3}{4}(x-0) \]

Answer 29

got it?

Answer 30

hope u got it.
gotta go.
bye

Answer 31

thanks got it (y)