Knowing that the equation will be perpendicular to the one given will only give us the slope. Perpendicular means that the slope will be opposite to what it is now.
The opposite of -4 (the current slope) is 1/4. Even knowing only this will tell us that the answer is b, but I will continue to explain for when no options are given.
Step 2: Y-intercept
Now that we know the slope, the perpendicular aspect of this equation will no longer be of any help.
To find the y-intercept, we need to substitute y and x with the point given.
Our current equation is— y= 1/4x+b
Let’s substitute the point into this. The point (-2,3) tells us that the y-value is 3 and the x-value is -2.
y= 1/4x+ b
3=1/4(-2)+b
3 = -1/2 +b +1/2 +1/2 __________ 3 1/2 =b
Step 3: Improper fraction
Being that it is preferred to leave fractions improper, let’s turn 3 1/2 into an improper fraction. This will turn into 7/2 (comment below if you need an explanation of how to do this)
Final answer: now that we know that the slope is 1/4 and the y-intercept is 7/2, we know that our equation will be y=1/4x+7/2
Hope this helps comment below for more questions:)
is a proper joint density function if, over its support, is non-negative and the integral of is 1. The first condition is easily met as long as . To meet the second condition, we require
b. Find the marginal joint density of and by integrating the joint density with respect to :
Then
c. This probability can be found by simply integrating the joint density:
