Respuesta :
Given:
Baseball is thrown at 89 miles per hour.
The ball will travel 324 feet when hit by a bat swung at 51 miles per hour.
It will travel 444 feet when hit by a boat swung at 81 miles per hour.
To find:
The addition distance travelled by the ball if the speed of bat increased by 1 unit.
Step-by-step explanation:
Let y be the number of feet traveled by the ball when hit by a bat swung at x miles per hour.
The ball will travel 324 feet when hit by a bat swung at 51 miles per hour. So, the point is (51,324).
It will travel 444 feet when hit by a boat swung at 81 miles per hour. So, the point is (81, 444).
Equation of line passes through two points is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-324=\dfrac{444-324}{81-51}(x-51)[/tex]
[tex]y-324=\dfrac{120}{30}(x-51)[/tex]
[tex]y-324=4(x-51)[/tex]
[tex]y-324=4x-204[/tex]
Add 324 on both sides.
[tex]y=4x-204+324[/tex]
[tex]y=4x+120[/tex]
Using the slope intercept form,
[tex]y=mx+b[/tex]
where, m is slope.
The slope of equation [tex]y=4x+120[/tex] is 4. It means, the ball will travel 4 feet farther for each mile-per-hour increase in the speed of the bat.
