Find the value of c such that the three points (5,5), (-3,1), and (6,c) lie on the same line. Note: Three points are on the same line if the slope of the line through any two points is always the same.

c = 5.5

Step-by-step explanation:

We can find the slope of the line using the given points (5,5) and (-3,1) using rise over run:

-4/-8 = 1/2

Now, we can plug in the slope and a point into the equation y = mx + b to find b:

5 = 1/2(5) + b

5 = 2.5 + b

2.5 = b

Then, we can plug in 6 in the point (6,c) to find c:

y = (1/2)(6) + 2.5

y = 3 + 2.5

y = 5.5

c = 5.5

c = 5.5

Step-by-step explanation:

Find the slope with two points

m = (y2-y1)/(x2-x1)

m = (1-5)/(-3-5)

   = -4/-8

   = 1/2

If all the points are on the same line, then they have the same slope

m = (y2-y1)/(x2-x1)

Using the first and third points

1/2 = (c-5)/(6-5)

1/2 =  (c-5)/1

1/2 = c-5

Add 5 to each side

5+1/2 = c

5.5 =c

you answer is a

step-by-step explanation:

part a

x     y

0     8

1     7.5

2     7

3     6.5

4     6

5     5.5  

for every hour i deducted .5 inches from the length of the candle

part b

it is a function because for every x value there is only one y value

part   c

for every x value there is only one y value

x       y

0       8

1       7.6

2       7.2

3       6.8

step-by-step explanation: