Extra a candle is 17 in tall after burning for 3 hours. after 5
hours, it is 15 in, tall. write a linear equation to
model the relationship between heighth of the candle and time t. predict how tall the candle will be after burning 8 hours? show your steps and explain your work: ))
everything you so much in

1)  

2) 12 inches tall.

Step-by-step explanation:

1) The equation of the line in Slope-Intercept form is:

Where "m" is the slope and "b" is the y-intercept.

In this case:

(The height of the candle in inches)

(The time in hours)

Then, we can rewrite it:

Based on the information provided in the exercise, the line passes through these points:

and

Then, we can find the slope of the line with the formula :

Now we need to substitute the slope and one of the points into    and then solve for "b":

Substituting values, we get that the a linear equation that models the relationship between the heigth of the candle and the time, is:

2) We must substitute into the linear equation   in order to find the height of the candle after burning 8 hours:

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

the two may have that, even a breakdown is probably offered