Question

Is the given function linear or nonlinear? If it is linear, determine the slope. Please show all of your work. (see attachment)

Answer 1

take a pair of coordinates and find the slope
and see if it the same if you take another pair

Answer 2

what

Answer 3

\[m_1=\frac{-11-1}{2-(-1)}\]
\[m_2=\frac{17-(-11)}{-5-2}\]
\[m_3=\frac{-31-17}{7-(-5)}\]
\[m_4=\frac{-15-(-31)}{3-7}\]
see if these slopes are the same
you can also make an equation given a point and see if you get the y given on your sheet for every x on your sheet

Answer 4

\[m_1=\frac{-12}{3}=-4\]
\[y=-4x+b\]
(2,-11)
-11=-4(2)+b
-11=-8+b
-11+8=b
b=-3
--------
y=-4x-3
f(x)=-4x-3

Answer 5

so plug in each x given on sheet your sheet and see if you get the same y on your sheet for each x you plug in

Answer 6

if you get the same y on your sheet for each x
then the function is linear since each point lies on the
line y=-4x-3

Answer 7

where did you get these equations

Answer 8

i got it from the first two coordinates you gave me as i showed above

Answer 9

oh..well i posted this because I have no idea how to do the problem.

Answer 10

so you don't understand anything i did?

Answer 11

not really. sorry :(

Answer 12

i found the slope given the first two coordinates

Answer 13

we know a point on the "line"
so i plugged in (2,-11) to find the y-intercept(=b)

Answer 14

ok

Answer 15

thank you myininaya. Even though I am still confused. :-/

Answer 16

do you know how to find an equation of a line given two points on that line?

Answer 17

I am not sure really. I tried to plug in the points into the formula you posted but for (-5, 17) I got this:
17=-4(-5)+b
17=20+b
17+20=b
b=37
y=4x+37

Where did I go wrong?

Answer 18

17=20+b
to solve for b subtract 20 on both sides
17-20=b
-3=b

Answer 19

ohhh ok. Thank you. I think I got it....so the slope would be -3? All of the answers are -3 so it would be linear. Is that correct?
Thank you for helping me. :)

Answer 20

line y=-4x-3
the slope of this line is -4
do all the points lie on this line?
if so then it is linear and the slope is -4

Answer 21

Great thank you so much. I think I finally have figured this out. :)