Question

math problem

Answer 1

so we have three different lines, do you see?

when we have x < -2

what is the equation for that line?
It's a straight line where all the values are 1

Answer 2

yep its a straihgt line

Answer 3

so what would that be?

y = what

Answer 4

1?

Answer 5

yes, now you can eliminate one answer choice

now let's look at the line in the middle

that's when the x values are
\(-2 \le x < 1\)

what is the equation of that line?

Answer 6

you don't need to figure out the exact line since they gave us answer choices

just tell me
does it have a positive slope or a negative slope?
and what is its y-intercept?

Answer 7

because remember it's a straight line so the equation is in the form of

y = mx + b

m is the slope
b is the y-intercept

Answer 8

h

Answer 9

im not sure

Answer 10

no no

we're not looking at the graph of that

what I wrote is the possible x-values

we're looking at the line in your image when x is between those values

\( -2 \le x < 1\) tells us that when x is between -2 and 1, the graph follows this equation

we're trying to find the middle line in your image

Answer 11

so hat should i do

Answer 12

What is the y-intercept of this line??

This is the line that falls between -2 and 1 which we wrote the domain as -2 \(\le\) x < 1

Answer 13

-1?

Answer 14

the y-intercept is where it crosses the y-axis

where does the line cross the y-axis?

and the equation of that line would be in the form

y = mx + b

where b is the y-intercept

Answer 15

-3

Answer 16

Good now look at your answer choices for that second equation

which has 1 listed for the for first x < -2
and has an equation with -3 as the y-intercept?

since it has y-intercept of -3 that means the equation would look something like
`mx - 3`

Answer 17

b?

Answer 18

That's correct

and if we calculated the slope of the second line, we would have found that the slope was 2

and if we went and calculated the equation of the third line, we would have found that it is -x+5
(it does have a negative slope and the y-intercept would be 5)

Answer 19

thanks

Answer 20

no problem