Question

Line a has an equation y=(m-3)x+3 , where m is any integer.
Line b has an equation y=-x+4

What is the value of m if line a is parallel to line b?

What is the value of m if line a is perpendicular to line b?

For what values of m will the slope of line lie between 0 and 4 (not including either value)? Drop the numbers in increasing order
(((the choices are 0-9)))

Answer 1

L1: y=(m-3)x+3
L2: y=-x+4
@guppy83711 Can you tell me the slopes of L1 and L2?

Answer 2

it dosnt say... it just says the slope is any integer @mathmate

Answer 3

@guppy83711
I expect you to give me the slope of each of the lines. It is necessary to know these quantities to solve the questions.

Answer 4

The slope of an equation of a line in slope-intercept form (same form as these equations)
y=ax+b,
then a is the slope, and b is the intercept.
Now can you give me the slopes of L1 and L2?

Answer 5

i dont get how to find line 1's slope but
L2 is -1
@mathmate

Answer 6

For L2, slope is -1.
What you need to do is to look for the coefficient of x.
If the coefficient is not a pure number, is is still the slope.
For L1, the coefficient of x in L1: (m-3)x+3
is what's left when the term (m-3)x is stripped off the x, what's left is (m-3), and so (m-3) is the slope of L2.
Remember we are working with algebra. Not all quantities are pure numbers. (m-3) is still a quantity which equals the slope.
Is that more clear?

Answer 7

Kind of... If (m-3) is the slope then how would i solve this?

Answer 8

"What is the value of m if line a is parallel to line b?"
If L1 and L2 are parallel, then their slopes are equal.
Can you solve for m then?

Answer 9

-1?

Answer 10

@mathmate

Answer 11

If they are parallel, the slopes are \(equal\).
So -1=m-3, can you solve for m?

Answer 12

m=2? @mathmate

Answer 13

That is correct!
Are you ready for the next question?

Answer 14

yea @mathmate

Answer 15

"What is the value of m if line a is perpendicular to line b?"
When two lines are perpendicular to each other, the product (times) of the two slopes equals -1.
i.e. (-1)(m-3)=-1
Can you solve for m ?

Answer 16

-4?

Answer 17

Hmmm let me see:
(-1)(-4-3)=(-1)(-7)=7 \(\ne\) -1
so m=-4 is not correct.
Can you try again, or show your work?

Answer 18

(-1)(4-3)=(-1)(1)=-1? m=4?

Answer 19

@mathmate

Answer 20

Yay, you got it again!
Are you ready for the next one?

Answer 21

Yes

Answer 22

"For what values of m will the slope of line lie between 0 and 4 (not including either value)? Drop the numbers in increasing order
(((the choices are 0-9)))"
Now you need to solve for the slope of L1 two times: once slope=0, find m, and
the other slope = 4, and find m.
Then you would write them in an interval, like (2,6) with the numbers that you find.
Get set, go!!

Answer 23

What?? i just got really confused...

Answer 24

Solve one at a time.
If L1 has a slope of 0, what's m?

Answer 25

I thought m was slope? @mathmate

Answer 26

m is not slope of L1. (m-3) is slope of L1, and that equals 0. What is m?

Answer 27

3

Answer 28

@mathmate

Answer 29

Correct!
Now go for slope of L1=4. What would m be?

Answer 30

1? @mathmate

Answer 31

(1-3)\(\ne\)4, so you'd have to try again! Sorry

Answer 32

Oh it is 7. I thought it was addition for some reason
@mathmate

Answer 33

ok.
So you got 1 and 7.
We need to put the numbers in an interval, in the form (a,b), where a is the smaller number, and b is the larger number.
We also have to exclude a and b (we were told to), so we put (a,b).
If we want to include a, we would write [a,b), or both, then [a,b].
Use 1 and 7 to write your interval and you're done! :)