On a coordinate plane, a line goes through (negative 3, 2) and (0, 1). A point is at (3, 4). What is the equation of the line th
2 answers:
Answer:
Step-by-step explanation:
step 1
Find the slope of the given line
we have
(-3,2) and (0,1)
The slope m is
step 2
Find the slope of the line perpendicular to the given line
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of its slopes is -1)
so
The slope is
step 3
Find the equation of the line in point slope form
we have
----> equation in point slope form
Convert to slope intercept form
You might be interested in
Answer:
The rate at which the distance from the plane to the station is increasing is 331 miles per hour.
Step-by-step explanation:
We can find the rate at which the distance from the plane to the station is increasing by imaging the formation of a right triangle with the following dimensions:
a: is one side of the triangle = altitude of the plane = 3 miles
b: is the other side of the triangle = the distance traveled by the plane when it is 4 miles away from the station and an altitude of 3 miles
h: is the hypotenuse of the triangle = distance between the plane and the station = 4 miles
First, we need to find b:
(1)
Now, to find the rate we need to find the derivative of equation (1) with respect to time:
Since "da/dt" is constant (the altitude of the plane does not change with time), we have:
And knowing that the plane is moving at a speed of 500 mi/h (db/dt):
Therefore, the rate at which the distance from the plane to the station is increasing is 331 miles per hour.
I hope it helps you!