a candle is a foot tall after burning an hour. after 4 h it is 10.5 in. tall. write a linear equation to model the height y of the candle after x hours. and how many hours will the candle be 6 inches tall??

plz explain the work .....

plz...help

look at it as ordered pairs of the form

(time, height)
you are given 2 such points, namely
(1,12) and (4,10.5)

slope = (10.5+12)/(4-1)
= -1.5/3 = -.5 or =1/2

using height = m(time) + b (remember y=mx+b ?)
and using the point (1,12)
we get
12 = -(1/2)(1) + b
b = 12.5

so height = -time/2 + 12.5

you want height to be 6
6 = -time/2 + 12.5
12 = -time + 25
time = 25-12
= 13

thanks so so so much

To write a linear equation to model the height of the candle after x hours, we need to find the equation of a straight line that passes through two points: (1, 12) and (4, 10.5).

Using the formula for a straight line, y = mx + b, where m represents the slope of the line and b represents the y-intercept, we can derive the equation.

First, we need to find the slope (m) by calculating the change in y divided by the change in x:

m = (10.5 - 12) / (4 - 1)
= -1.5 / 3
= -0.5

Next, we can substitute one of the points (1, 12) into the equation and solve for the y-intercept (b):

12 = -0.5 * 1 + b
12 = -0.5 + b
b = 12 + 0.5
b = 12.5

Therefore, the linear equation that models the height of the candle after x hours is:

y = -0.5x + 12.5

To find the number of hours it will take for the candle to be 6 inches tall, we set y to 6 in the equation and solve for x:

6 = -0.5x + 12.5
-0.5x = 6 - 12.5
-0.5x = -6.5
x = (-6.5) / (-0.5)
x = 13

Thus, the candle will be 6 inches tall after 13 hours.