Answer:
[tex]y=-0.2x+15\\ \\15\ inches[/tex]
Step-by-step explanation:
Let
x = time (number of hours the cande was burning)
y = height of the candle after x hours of burning
A candlestick burns at a rate of 0.2 inches per hour. This means the slope of the linear function is [tex]m=-0.2[/tex]
The equation of the linear function is
[tex]y=-0.2x+b[/tex]
After 8 straight hours of burning, the candlestick is 13.4 inches tall. This means x = 8 and y = 13.4, then
[tex]13.4=-0.2\cdot 8+b\\ \\b-1.6=13.4\\ \\b=13.4+1.6\\ \\b=15[/tex]
Hence, the equation of the linear function is
[tex]y=-0.2x+15[/tex]
Initially, at x = 0, the height of the candle was
[tex]y=-0.2\cdot 0+15\\ \\y=15\ inches[/tex]
