Question

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

Explanation:

Step1: Recall y-intercept formula

The y - intercept of a linear function in the form \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept) is the value of \(y\) when \(x = 0\). For the given function \(y=12 - 0.2x\), we can rewrite it in the form \(y=- 0.2x + 12\), so the y - intercept \(b = 12\).

Step2: Interpret the y - intercept

When \(x = 0\), \(x\) represents the number of hours the candle has burned. If \(x = 0\), the candle has not burned at all. Substituting \(x = 0\) into the equation \(y = 12-0.2x\), we get \(y=12-0.2(0)=12\). So \(y = 12\) when \(x = 0\) means the amount of the candle (in ounces) before it starts burning (when 0 hours of burning have occurred) is 12 ounces.

Now let's analyze the options:

• Option A: The ounces burned each hour is the slope (\(- 0.2\)), not the y - intercept, so A is wrong.
• Option B: The y - intercept is 12, and it represents the ounces in the candle before it burns (when \(x = 0\)), this is correct.
• Option C: The y - intercept is not \(-0.2\), and \(-0.2\) is the slope (rate of burning per hour), not the initial amount, so C is wrong.
• Option D: \(-0.2\) is the slope (ounces burned per hour), but the y - intercept is 12, so D is wrong.

Answer:

B. 12; the ounces in the candle before it burns