Question

write two equations for two perpendicular lines that have the same y-intercept and do now pass through the origin.

Answer 1

you probably mean do NOT pass through origin right?

Answer 2

not pass through the origin*

Answer 3

well do you know what it means for one line to be perpendicular to another?

Answer 4

at a 90 degree angle?

Answer 5

Exactly! Now do you know the general equation for a line?

Answer 6

no

Answer 7

It's y = ax + b, where a and b are any real number. Does that equation look familiar?

Answer 8

yes, what numbers would i put?

Answer 9

any number you want! That's the beauty of this equation. Now give me an example of a line given that equation.

Answer 10

but they numbers have to have the same y-intercept and do now pass through the origin.

Answer 11

yes I will get to that but I want to make sure you understand this first.

Answer 12

y = 4x+5
and
y=4x+3

Answer 13

nice those are all lines, now there's a particular reason why lines are generally given in that form(y=ax+b). The reason is that the number that you put for a is the slope of the line and b is the y-intercept. So now that you know that, give me 2 lines that have the same y-intercept.

Answer 14

y=3x+5
y=4x+5

Answer 15

good! Now do you understand the concept of slope?

Answer 16

yeah, but i dont know how to not make the numbers go through the origin

Answer 17

do you understand what it means for the slope if two lines are perpendicular?

Answer 18

no

Answer 19

ok so first off I'll say this, the fact that the lines have a y-intercept (aka b does not equal 0) means that it doesn't go through the origin. So you don't have to worry about that (i'll show you this later). But for now explain to me what the slope of the line is.

Answer 20

wait so i could just use any number for a and it still wouldnt go through the origin?

Answer 21

yup. Think about it, what does it mean for a line to go through the origin?

Answer 22

to go through 0. i undrstand now

Answer 23

ok cool so what does the slope of a line mean?