Question

Is it possible for line ax + by = c to lack a y-intercept? To lack an x-intercept? Explain.

Answer 1

think about this a bit. if a line never intersected the y axes - what can you say about it?

Answer 2

It's vertical.

Answer 3

correct - or in other words, it is parallel to the y axes

Answer 4

similar thing holds for a line that never intersects the x axes

Answer 5

i.e. it must be horisontal, or in other words, parallel to the x axes

Answer 6

Okay....I understand. So yes, it is possible.

Answer 7

correct - can you think of what the equation of a vertical line would look like?

Answer 8

y= _____

Answer 9

in terms of the symbols that were given to you above

Answer 10

what can you say about the value of x anywhere on a vertical line?

Answer 11

The value of x could increase or decrease depending on the direction.

Answer 12

y= ____ is horizontal....isn't it?

Answer 13

on any "given" vertical line, would the value of x change along that line?

Answer 14

On a vertical line, the x is constant.

Answer 15

correct, so its equation would be something like: ax = c

(using the symbols given in your question)

which could simplify to just: x = k where k is some constant

Answer 16

similar principal for a horizontal line

Answer 17

for horizontal, would it be like by=c then?

Answer 18

correct! :)

Answer 19

Okay, thank you for your help!

Answer 20

yw :)

so the full answer to your question would be something like:

it can lack a y intercept if a=0
it can lack a x intercept if b=0

Answer 21

(sorry - that should be the other way around)

Answer 22

it can lack a y intercept if b=0
it can lack a x intercept if a=0