Verified Answer :

apologiabiology

rate of change is also knkown as slope which is found by
\(\frac{y2-y1}{x2-x1}\)=slope if you know 2 points/ordered pairs
aos, if x incheases while y decreases then slope is negative
when x increases while y increases then slpe if positive
also, if you can convert to y=mx+b, m=slope
another thing if you have ax+by=c then slope=-a/b

so first one
2x-5y=15
a=2
b=-5
-2/-5=2/5
slope=2/5
positive

next
y=-4x
-4 =slope=negative


x increases while y decreases
negative

x increases while y decreases
negative


so
Positive
Negative
Negative
Negative





A. 6x-3y=12
sloope=-6/-3=2

B. y=5x+b
slope=5

C. (8-2)/(3-1)=6/2=3
sloope=3

D. goes up 4 units and goes right 1 unit, 4/1=4
sloope=4


5 is greates
B is the answer









A. (6-3)/(4-3)=3/1=3
slope=3

B. y=4+6x
slope=6


C.12x+6y=18
slope=-12/6=-2

D. goes down 5 units as it goest 1 uniit to right aka -5./1
slope=-5


greatest is 6
B is answer











the starting value I would guess si when x=1 what is the greats y value

look at each
first one
A. x=1 and =-3

B.y=3x-8
y=3(1)-8
y=3-8
y=-5

C. 8x+4y=16
8(1)+4y=16
8+4y=16
4y=8
y=2

D. at 1 unit to right it is 1 nit up so y=1


greatest is  2 or C





so just subsitute 1 for x since x represents how many teaspoons
y=16(1)560
y=16+560
y=576 caloris for 1 sugar teaspoon

for honey, just read off the graph
for when x=1
y=504

so calores of sugar=576
calories in honey=504






ANSWERS

Postive
Negative
Negative
Negative

B

B

C

sugar=576
honey=504

1) A negative rate of change is when the slope is a negative number...so, lets look for the slope that is negative. 

1.  2x - 5y = -15 
   -5y = -2x - 15
    y = 0.4  + 5
Positive 

2.  y = -4x + 9
    Negative

3. -16 - - 10 / 4 - 2 = m
m = -6/2
m = -3
Negative

4. 11 - 15  / -2 - - 3
     -4 / 1 = -4
m = -4
Negative 

Done with number one! :P

2) The greatest rate of change would be the steepest line, so lets find that!

From the answer choices, '5' has the largest slope. 

Answer: B) y = 5x + 4

3) Now, again, we must find the greatest rate of change. 

A) 6 - 3 / 4-3
m = 3/1
m = 3

B) m = 6

C) m = -2

We see that 6 is the greatest. 

Answer: B) 

4) Greatest start value would be the y intercept.

C has the greatest start value, because it is 2, so that would be the answer. 

Answer: c

5) y=16*1 + 560
y=16+560
y=576 

x = 1
y = 504

Calories of sugar would be >>>>>>>>>>>>>  576
Calories in honey would be >>>>>>>>>>>>>> 504

I HOPE THIS HELPED YOUUUUUU

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