Anew line is drawn through the point (-3,6) and perpendicular to the line with x-intercept (3,0) and y intercept (0,3) . what is the equation of this new line ?

The equation of the new line is  or  

Step-by-step explanation:

step 1

Find out the slope of the line with x-intercept (3,0) and y intercept (0,3)

The formula to calculate the slope between two points is equal to

substitute the values

step 2

Find the slope of the new line perpendicular to the given line

we know that

If two lines are perpendicular,then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

we have

----> slope of the given line

so

---> slope of the new line

step 3

Find the equation of the new line in point slope form

we have

substitute

----> equation in point slope form

Convert to slope intercept form

isolate the variable y

The point of intersection of these two equation is 1 , 6

Step-by-step explanation:

Given as :

The two equation of line are

y = 4 x + 2                ........1

y = - x + 7                 ........2

Let The point of intersection of these two equation = p ( )

Now, solving the equation 1 and 2

So, 4 x + 2 = - x + 7

Or, 4 x + x = 7 - 2

Or, 5 x = 5

∴ x =

i.e  x = 1

Again

put the value of x in eq 2 , we get

∵ y = - x + 7

Or, y = - 1 + 7

Or, y = 6

so, The point of intersection of these two equation = p ( ) = 1 , 6

Hence. The point of intersection of these two equation is 1 , 6 Answer