1 Find the slope of the line that has the following intercep

1. Find the slope of the line that has the following intercepts: y-intercept: -10: x-intercept: 3

2. Suppose that an object is projected in such a way that its height above the ground in feet after t seconds is given by s(t)= -16t^2+48t+37. Find the maximum height of the object.

Solution

1) y-intercept: -10:

Point ( 0, -10 )

x-intercept: 3

Point ( 3, 0)

slope from the two points (-10 -0)/(0 - 3) = 10/3

2) s(t)= -16t^2+48t+37

Its a quadratic equation , vertex gives the maximum height

t = b/2a = -48/-32 = 6/4 = 1.5 sec

Plug t = 1.5 sec to get maximum height:

s( 1.5) = -16(1.5)^2 +48(1.5) +37

= 73 feet