Write the equation of the line that is perpendicular to the line 5y=x−5 through the point (-1,0).
a. y= 1/5x+5
b. y= 1/5x−5
c. y= −5x−5
d. y= −5x+5

Steps:

---> Re arrange equation to get the format: y = mx + c

---> Work out the perpendicular gradient from the first equation

----> Substitute the x and y coordinates of point (-1, 0) and the perpendicular      gradient into y = mx + c   and work out c

---> Finally, substitute the perpendicular gradient and the value for c into y =mx + c  to get the gradient of the perpendicular line:

__________________________________________

Rearranging equation into the format: y = mx + c:

                 (Just divide both sides by y)

___________________________________________

Working out the perpendicular gradient:

To work out the perpendicular gradient, we just take the negative reciprocal of the gradient of

Note: negative reciprocal means we just flip the fraction and put a minus sign.

The regular gradient is:

So the perpendicular gradient is the negative reciprocal of

which is -5       (note: is just 5-)

___________________________________________

Now lets substitute in the values for the gradient (m), the y coord (0) and x coord (-1) of the point (-1, 0)   into y = mx + c, and solve for c:

y = mx + c     (substitute in all known values)

0 = -5(-1) + c   (the -1 times -5 will make + 5)

0 = 5 + c        (subtract 5 from both sides to cancel out the + 5)

-5 = c

so c = -5

____________________________________________

Finally, just substitute in the perpendicular gradient and the value for c into y = mx + c   to get the equation of the perpendicular line:

y = mx + c        (substitute in the perp. gradient and c)

y = -5x - 5

____________________________________________________

The equation to the line perpendicular to 5y = x - 5 through point (-1, 0) is :

C. y = -5x - 5

_______________________________________________

A quicker way to get equation of the perpendicular line once you know the perp. gradient is to use the equation:

y - y1 = m (x - x1)

y1 is the y coordinate of (-1, 0)

x1 is the x coordinate of (-1, 0)

m is the perpendicular gradient.

y - y1 = m (x - x1)       (Substitute in values)

y - 0 = -5 ( x - - 1)       (simplify)

y = -5 (x + 1)              (expand the brackets)

y = -5x - 5

5/6

step-by-step explanation:

if i remember correctly with perpendicular stuff you just take away the negative

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !