Question

Write an equation in slope intercept form to model the situation.

Answer 1

Answer:

$y=-\frac{1}{2}x + 10$

Step-by-step explanation:

Slope intercept form is a way of modeling a quadratic equation, where the coefficient of the term ($x$) is the slope (change) of the line, and the constant is the y-intercept. In essence;( $y=mx+b$ ), where ($m$) is the slope and ($b$) is the y-intercept.

The slope of the given line is ($-\frac{1}{2}$) because, this is the rate at which the candle burns, therefore, it is the change in the line. The change is ($\frac{1}{2}$) because this is the rate of burning, the slope is also negative since the height is decreasing. ($10$) is the y-intercept because it is the starting height of the candle. One will take the time since the start of burning the candle, multiply it by the slope, and add it to the y-intercept to find the current height of the candle. Therefore, the equation is ($y=-\frac{1}{2}x + 10$), where the output ($y$) is the current height of the candle, and the input ($x$) is the time at which the measruement was taken.