The bus is 54.5 miles far from the site at the time of 11:30A.M as per the given information in the question.
<h3>What is the slope of a line?</h3>
The slope of a line indicates how steep it is. Slope is defined mathematically as "climb over run" (change in y divided by change in x).
It is assumed that a bus moving at a constant speed departs at 10 a.m. towards a historic location, is 100 miles away by 10:25 a.m., and is 65 miles away at 11:15 a.m.
We must create a point-slope equation that connects the distance from the place to the time in minutes after 10:00 a.m. Then, around 11:30 a.m., we need to figure out how far the bus is from the site.
A line's point-slope is y₂-y₁)=m(x₂-x₁)
Since x denotes the amount of minutes after 10:00 a.m., 10:25 a.m. is represented by x=25 and 11:15 a.m. by x=75.
At 10:25 a.m., a distance of 100 miles from the place is represented by 75.
The point represents a distance of 100 miles from the site at 10:25 a.m. The point represents a distance of 65 miles from the site at 11:15 a.m.
By substituting the points (25, 100) and (75, 65) into the slope formula and simplifying we get,
m=(y₂-y₁)/(x₂-x₁)
m=(65-100)/(75-25)
m=-35/50
m=-0.7
Now choose one of the points and substitute that point and the slope into the slope-point form
y₋y₁=m(x-x₁)
By choosing (x₁, y₁)=(25, 100)
By choosing (x₂, y₂)=(75, 65)
Since 11:30 A,M is 90 minutes after 10:00A.M
By substituting x=90 in the equation we get the value of y,
y-100= -0.7(90-25)
y-100= -0.7(65)
y-100 =-45.5
y= 54.5
Hence, the bus is 54.5 miles from the site at the time of 11:30 A.M
y-100= -0.7(x-25)
OR
y-65= -0.7(x-75)
The bus is 54.5 miles from the site at 11:30A.M.
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where r is the radius of the circle