Answer: The required equation representing the given situation is [tex]y=-14.8x+15.[/tex]
Step-by-step explanation: Given that a candle stick burns at the rate of 0.2 inches per hour . After eight straight hours of burning the candle stick is 13.4 inches tall
We are to write the linear equation in slope-intercept form y = mx + c.
Let us consider that number of hours as x co-ordinates and corresponding length of the candle burnt as y co-ordinates.
Since after 8 hours, the candle is 13.4 inches tall, so in 0 hours, the height of the candle was
[tex]13.4+8\times0.2=13.4+1.6=15.[/tex]
So, the linear function will pass through two points (1, 0.2) and (0, 15).
We know that
the slope of a line passing through the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
So, the slope of the given linear function will be
[tex]m=\dfrac{15-0.2}{0-1}=\dfrac{14.8}{-1}=-14.8.[/tex]
Since the function passes through the point (0, 15), so its equation will be
[tex]y-15=m(x-0)\\\\\Rightarrow y-15=-14.8x\\\\\Rightarrow y=-14.8x+15.[/tex]
Thus, the required linear equation representing the given situation is [tex]y=-14.8x+15.[/tex]
