a road crew must clear a hill that is 110.0 feet tall so that a new road can be built, they are to clear 11 1/2 feet of the hill each day, find the equation in slope intercept on the line that represent to height
Let x = number of days
Let y = height cleared after x days
If they can clear 11.5 ft per day, the height cleared in x days is:
y = 11.5x
To find the equation in slope-intercept form that represents the height of the hill as a function of the number of days, we need to determine the slope and the y-intercept.
Let's assume "y" represents the height of the hill in feet, and "x" represents the number of days. Given that the road crew clears 11 1/2 feet of the hill each day, we can say that the slope is -11.5.
Since the road crew is starting with a hill that is 110.0 feet tall and clearing 11 1/2 feet each day, the initial height of the hill would be the y-intercept. Let's call it "b."
Using the point-slope formula, the equation in slope-intercept form can be written as:
y = mx + b
where:
m = slope
x = number of days
y = height of the hill
Substituting the values, we have:
y = -11.5x + b
To find the value of "b", we substitute the given information that the road crew starts with a hill that is 110.0 feet tall when x = 0 (the initial number of days):
110 = -11.5(0) + b
110 = b
Therefore, the equation in slope-intercept form that represents the height of the hill as a function of the number of days is:
y = -11.5x + 110