Question

24 this equation shows the amount of a candle that is left (in ounces) after burning for x hours. what is y-intercept for this function, and what does it represent?
y = 12 - 0.2x
a 12; the ounces burned each hour
b 12; the ounces in the candle before it burns
c -0.2; the ounces in the candle before it burns
d -0.2; the ounces of the candle that burn each hour
len chose d as the correct answer. how did he get that answer?

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. In the equation \(y=12 - 0.2x\), we can rewrite it as \(y=- 0.2x + 12\).

Step2: Analyze Len's mistake

Len probably confused the slope and the \(y\) - intercept. The coefficient of \(x\) (\(-0.2\)) is the slope, which represents the rate of change (the ounces of the candle that burn each hour). The \(y\) - intercept is \(12\), which represents the initial amount of the candle (ounces in the candle before it burns). But Len thought that the \(y\) - intercept was \(-0.2\) (the slope) and associated the slope's meaning (ounces burned per hour) with the \(y\) - intercept. So he misidentified the \(y\) - intercept as \(-0.2\) and then used the meaning of the slope (ounces burned per hour) to describe it, leading him to choose option D.

Answer:

Len confused the slope and the \(y\) - intercept. He took the slope (\(-0.2\), which represents ounces burned per hour) as the \(y\) - intercept and matched its meaning to the \(y\) - intercept's description, so he chose D.