Question
Question
After a blizzard, 18 inches of snow sat on Maggie's driveway. She measured the snow each hour and determined that it was melting at a rate of 0.5 inches per hour. Which equation best fits this situation in slope intercept form?
After a blizzard, 18 inches of snow sat on Maggie's driveway. She measured the snow each hour and determined that it was melting at a rate of 0.5 inches per hour. Which equation best fits this situation in slope intercept form?
Answers
Answered by
GPT-4o mini
To represent the situation in slope-intercept form, we first need to identify the components of the linear equation. The slope-intercept form of a line is given by the equation:
\[ y = mx + b \]
where:
- \( y \) is the amount of snow remaining,
- \( m \) is the slope (the rate at which the snow is melting),
- \( x \) is the time in hours,
- \( b \) is the y-intercept (the initial amount of snow).
From the problem, we have:
- The initial amount of snow (when \( x = 0 \)) is 18 inches, so \( b = 18 \).
- The snow is melting at a rate of 0.5 inches per hour, which represents the slope \( m \). Since the snow is melting, the rate will be negative: \( m = -0.5 \).
Now, substituting the values into the equation:
\[ y = -0.5x + 18 \]
Thus, the equation that best fits this situation in slope-intercept form is:
\[ y = -0.5x + 18 \]
\[ y = mx + b \]
where:
- \( y \) is the amount of snow remaining,
- \( m \) is the slope (the rate at which the snow is melting),
- \( x \) is the time in hours,
- \( b \) is the y-intercept (the initial amount of snow).
From the problem, we have:
- The initial amount of snow (when \( x = 0 \)) is 18 inches, so \( b = 18 \).
- The snow is melting at a rate of 0.5 inches per hour, which represents the slope \( m \). Since the snow is melting, the rate will be negative: \( m = -0.5 \).
Now, substituting the values into the equation:
\[ y = -0.5x + 18 \]
Thus, the equation that best fits this situation in slope-intercept form is:
\[ y = -0.5x + 18 \]