Question

the equations represent the heights of two candles that burn at omari’s dinner table. each equation shows the height in inches, y, as a function of time in minutes, x. the rate of change is the same for each function. the height of the candles decreases at a rate of \\(\frac{1}{10}\\) inch per minute. candle a: \\(-\frac{1}{10}x + 2\\) candle b: \\(-\frac{1}{10}x + 8\\) what is the height of each candle when it is lit? find the initial value of each function. candle a initial value: ? candle b initial value: ?

Explanation:

Step1: Recall the slope - intercept form of a linear equation

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope (rate of change) and \(b\) is the \(y\) - intercept (initial value).

Step2: Identify the initial values for Candle A and Candle B

For Candle A, the equation is \(y=-\frac{1}{10}x + 2\). Comparing with \(y = mx + b\), when \(x = 0\) (at the start, when the candle is lit), \(y=b\). So the initial value of Candle A is \(2\).
For Candle B, the equation is \(y=-\frac{1}{10}x + 8\). Comparing with \(y = mx + b\), when \(x = 0\) (at the start, when the candle is lit), \(y=b\). So the initial value of Candle B is \(8\).

Answer:

Candle A initial value: \(2\)
Candle B initial value: \(8\)